Decoding apparatus and decoding method

ABSTRACT

A decoding apparatus and method are capable of decoding LDPC codes with a high degree of precision while preventing the circuit scale of the decoding apparatus from increasing. A computation section carries out a first computation process corresponding to three check-node processes by making use of decoding intermediate results supplied from a decoding intermediate result storage memory by way of a cyclic shift circuit, and stores the result of the first computation process in a decoding intermediate result storage memory. A computation section carries out a second computation process corresponding to six variable-node processes by making use of decoding intermediate results supplied from a decoding intermediate result storage memory by way of a cyclic shift circuit, and stores the decoding intermediate result in the decoding intermediate result storage memory.

TECHNICAL FIELD

The present invention relates to a decoding apparatus and a decodingmethod. More particularly, the present invention relates to a decodingapparatus and a decoding method, which are used for decoding codesobtained as a result of a coding process producing low density paritycheck codes (LDPC coding).

BACKGROUND ART

In recent years, researches in fields including communication fieldssuch as the mobile-body communication and the deep-space communicationas well as broadcasting fields such as the terrestrial wave broadcastingand the satellite digital broadcasting have been making very goodprogress. Accompanying these researches, studies of coding theories arealso well conducted with the intention of increasing the efficiencies oferror correction coding and error correction decoding.

A Shannon limit given by the so-called communication line coding theoremestablished by C. E. Shannon is known as a theoretical limit of codingperformances. Studies of coding theories are conducted with theintention of developing codes demonstrating a performance close to theShannon limit. In recent years, a technique known as the so-called turbocoding technique is being developed as a coding method demonstrating aperformance close to the Shannon limit. The turbo coding technique is,for example, a coding technique such as PCCCs (Parallel ConcatenatedConvolutional Codes) and SCCCs (Serially Concatenated ConvolutionalCodes). While turbo codes are being developed, low density parity checkcodes are attracting a great deal of attention. Referred to hereafter asLDPC codes, the low density parity check codes are codes used in acoding method, which has been known since an early time in the past.

The LDPC codes were first proposed in a document authored by R. G.Gallager with a title of “Low Density Parity Check Codes,” as a documentpublished by M. I. T. Press in the year of 1963 in Cambridge, Mass.Later on, the LDPC codes again drew lots of attention as described indocuments such as a document authored by D. J. C. Mackay with a title of“Good error correcting codes based on very sparse matrices” as adocument submitted to IEEE Trans. Inf. Theory, IT-45, pp. 399-431, 1999and a document authored by M. G. Luby, M. Mitzenmacher, M. A.Shokrollahi and D. A. Spielman with a title of “Analysis of low densitycodes and improved designs using irregular graphs” in Proceedings of ACMSymposium on Theory of Computing, pp. 249-258, 1998.

Researches conducted in recent years are also clarifying the fact that,by increasing the code length of the LDPC codes, it is possible todisplay a performance close to the Shannon limit in the same way as theturbo codes or the like. In addition, the LDPC codes exhibit a propertyshowing that the minimum distance is proportional to the code length.Thus, the LDPC codes offer merits that the LDPC codes have a good blockerror probability characteristic as one of its characteristics and theso-called error floor phenomenon hardly occurs in the LDPC codes. Theerror floor phenomenon is a phenomenon observed in decodingcharacteristics of the turbo codes or the like.

The LDPC codes are explained concretely as follows. It is to be notedthat the LDPC codes are linear codes but are not necessarily2-dimensional codes. In the following description, however, the LDPCcodes are explained as 2-dimensional codes.

The most peculiar characteristic of the LDPC codes is the fact that aparity check matrix defining the LDPC codes is a sparse matrix. A sparsematrix is a matrix having a very small number of matrix elements eachset at “1”. Let notation H denote a sparse parity check matrix. In thiscase, as shown in FIG. 1, a typical sparse matrix H has a humming weightof “3” for each column and a humming weight of “6” for each row.

LDPC codes defined by a parity check matrix H having a constant hammingweight for each row and a constant hamming weight for each column asdescribed above are referred to as regular LDPC codes. On the otherhand, LDPC codes defined by a parity check matrix H having a hammingweight varying from row to row and a hamming weight varying from columnto column are referred to as irregular LDPC codes.

A LDPC-code encoding process is implemented to produce a generationmatrix G on the basis of the parity check matrix H and generate codewords by multiplying the generation matrix G by a 2-dimensionalinformation message. To put it concretely, first of all, a codingapparatus for carrying out an LDPC-code encoding process finds ageneration matrix G for which the equation GH^(T)=0 holds true, wherenotation H^(T) denotes the transposed matrix of the parity check matrixH. In this case, if the generation matrix G is a k×n matrix (that is, amatrix having k rows and n columns), the parity check matrix H is an(n−k)−row×n-column matrix.

If an n-bit code word c is an organization code matching a bit sequenceincluding a k-bit information message u and (n−k) parity bits followingthe information message u for example, the (n−k)−row×n-column paritycheck matrix H includes an information portion and a parity portion.Associated with the k-bit information message u of the code word chaving n bits, the information portion is a matrix portion having (n−k)rows and k columns. Associated with the (n−k) parity bits of the n-bitcode word c, the parity portion is a matrix portion having (n−k) rowsand (n−k) columns. In this case, if the parity portion is an uppertriangular matrix or a lower triangular matrix, the process to code theinformation message u into LDPC codes can be carried out by making useof the parity check matrix H.

That is to say, for example, the parity check matrix H has aninformation portion and a parity portion, which is a lower trianglematrix as shown in FIG. 2. If all the elements of the lower trianglematrix of the parity portion are set at 1, the first one of the paritybits included in the code word c has a value obtained as a result ofcarrying out EXOR (exclusive logical sum) operations on elements eachset at 1 on the first row of the information portion included in theparity check matrix H as a matrix portion associated with theinformation message u.

By the same token, the second one of the parity bits included in thecode word c has a value obtained as a result of carrying out EXORoperations on elements each set at 1 on the second row of theinformation portion included in the parity check matrix H as a matrixportion associated with the information message u and the first one ofthe parity bits.

Likewise, the third one of the parity bits included in the code word chas a value obtained as a result of carrying out EXOR operations onelements each set at 1 on the third row of the information portionincluded in the parity check matrix H as a matrix portion associatedwith the information message u and the first and second ones of theparity bits.

Thereafter, similarly, the ith one of the parity bits included in thecode word c has a value obtained as a result of carrying out EXORoperations on elements each set at 1 on the ith row of the informationportion included in the parity check matrix H as a matrix portionassociated with the information message u and first to (i−1)th ones ofthe parity bits.

The values of the (n−k) parity bits are found as described above, andthe (n−k) parity bits are placed at a location following the informationmessage u having k bits in order to create the code word having n bits.

A technique for decoding LDPC codes can be carried out by adoption of analgorithm proposed by Gallager as an algorithm referred to as aprobabilistic decoding algorithm. The probabilistic decoding algorithmis a message passing algorithm based on belief propagation on theso-called Tanner graph including variable nodes also referred to asmessage nodes and check nodes. In the following description, thevariable nodes and the check nodes may be properly referred to simply asnodes.

In a probabilistic decoding process, however, a message exchangedbetween nodes is a real number. Thus, in order to analyze the message,it is necessary to keep track of nothing but the probabilisticdistribution of the message having a continuous value. That is to say,it is necessary to carry out an analysis entailing a very high level ofdifficulty. In order to solve this problem, Gallager proposed algorithmsA and B as algorithms for decoding LDPC codes.

In general, a process for decoding LDPC codes is carried out inaccordance with a procedure like one represented by a flowchart shown inFIG. 3. It is to be noted that, in the flowchart representing theprocedure, notation U_(o) (u_(oi)) denotes a received value, notation ujdenotes a message output from a check node and notation v_(i) denotes amessage output from a variable node. In this case, a message is a realnumber expressing the “0” likelihood of a value in terms of theso-called log likelihood ratio. In addition, the log likelihood ratioexpressing the “0” likelihood of the received value U_(o) is representedas received data u_(oi).

As shown in the flowchart of FIG. 3, the procedure for decoding LDPCcodes begins with a step S11 at which a value U_(o) (u_(oi)) isreceived. At the same step, a message u_(j) and a variable k areinitialized to 0. The variable k is used as a repetition processingcounter taking an integer. Then, the flow of the procedure goes on to astep S12. At the step S12, a message v_(i) is found in accordance withEq. (1) based on the received value U_(o) (u_(oi)). Then, a messageu_(j) is found in accordance with Eq. (2), which is based on the messagev_(i).

$\begin{matrix}\left\lbrack {{Eq}.\mspace{14mu} 1} \right\rbrack & \; \\{v_{i} = {u_{0i} + {\sum\limits_{j = 1}^{d_{v} - 1}\; u_{j}}}} & (1) \\\left\lbrack {{Eq}.\mspace{14mu} 2} \right\rbrack & \; \\{{\tanh\left( \frac{u_{j}}{2} \right)} = {\prod\limits_{i = 1}^{d_{c} - 1}\;{\tanh\left( \frac{v_{i}}{2} \right)}}} & (2)\end{matrix}$

Notation d_(v) used in Eq. (1) denotes a parameter representing thenumber of elements arranged in the vertical direction (or the rowarrangement direction) of the parity check matrix H as elements each setat “1”. On the other hand, notation d_(c) used in Eq. (2) denotes aparameter representing the number of elements arranged in the horizontaldirection (or the column arrangement direction) of the parity checkmatrix H as elements each set at “1”. The parameters d_(v) and d_(c) canbe selected arbitrarily. In the case of a (3, 6) code for example, theparameter d_(v) is set at 3 (or d_(v)=3) whereas, the parameter d_(c) isset at 6 (or d_(c)=6).

It is to be noted that a message input from an edge for which a messageis to be output is not used as an addition or multiplication parameterin the computation according to Eq. (1) or (2) respectively. Thus, therange of the summation operation according to Eq. (1) is from 1 to(d_(v)−1) whereas the range of the multiplication operation according toEq. (2) is from 1 to (d_(c)−1). In addition, the multiplicationoperation according to Eq. (2) is actually carried out by creating atable showing values of a function R (v₁, v₂) expressed by Eq. (3) inadvance and using the value of the function R continuously (orrecursively) as shown in Eq. (4). The function R (v₁, v₂) has two inputsv₁ and v₂, generating one output as the value of the function.[Eq. 3]x=2 tan h ⁻¹[ tan h(v ₁/2)tan h(v ₂/2)]=R(v ₁ ,v ₂)  (3)[Eq. 4]u _(j) =R(v ₁ ,R(v ₂ ,R(v _(d) _(c) ₋₂ ,v _(d) _(c) ₋₁))))  (4)

At the step S12, the variable k is also incremented by “1”. Then, theflow of the procedure goes on to a step S13. At the step S13, thevariable k is compared with a repetitive-decoding count N determined inadvance in order to produce a result of determination as to whether ornot the variable k is at least equal to the repetitive-decoding count N.If the determination result produced in the process carried out at thestep S13 indicates that the variable k is smaller than therepetitive-decoding count N, the flow of the procedure goes back to thestep S12 in order to repeat the processes of the step S13 and thesubsequent steps in the same way as before.

If the determination result produced in the process carried out at thestep S13 indicates that the variable k is at least equal to therepetitive-decoding count N, on the other hand, the flow of theprocedure goes on to a step S14 at which a process according to Eq. (5)is carried out in order to find and output a message v as an eventualoutput decoding result. Then, the execution of the procedure fordecoding LDPC codes is ended.

$\begin{matrix}\left\lbrack {{Eq}.\mspace{14mu} 5} \right\rbrack & \; \\{v = {u_{0i} + {\sum\limits_{j = 1}^{d_{v}}\; u_{j}}}} & (5)\end{matrix}$

The process according to Eq. (5) is different from the process accordingto Eq. (1) in that the process according to Eq. (5) is carried out bymaking use of input messages from all edges connected to the variablenodes.

In the case of a (3, 6) code for example, such a process for decodingLDPC codes is carried out by exchanging messages between nodes as shownin FIG. 4. In a node marked with the “=” special character as shown inFIG. 4 to indicate that the node is a variable node, a computationprocess according to Eq. (1) is carried out. In a node marked with the“+” to indicate that the node is a check node, on the other hand, acomputation process according to Eq. (2) is carried out. Particularly,in accordance with the algorithm A, messages are each converted into a2-dimensional message. In every node marked with the “+”, an exclusivelogical summation process is carried out on (d_(c)−1) input messages. Inevery node marked with the “=”, on the other hand, for a received valueR, if (d_(v)−1) input messages are all different bit values, the code isinverted before being output.

In addition, also in recent years, a method for implementing thetechnique for decoding LDPC codes is being studied as well. Before themethod for implementing the technique for decoding LDPC codes isexplained, first of all, modeling of the technique for decoding LDPCcodes is described.

FIG. 5 is a diagram showing a typical parity check matrix H defining (3,6) LDPC codes having a coding rate of ½ and a code length of 12. Theparity check matrix H can be expressed by making use of a Tanner graphshown in FIG. 6. In the Tanner graph shown FIG. 6, a node marked withthe “+” special character is a check node whereas a node marked with the“=” special character is a variable node. The check and variable nodescorrespond respectively to the rows and the columns of the parity checkmatrix H. A line connecting a check node to a variable node is referredto as an edge corresponding to a matrix element set at “1” in the paritycheck matrix H. That is to say, if a matrix element located at theintersection of the jth row and the ith column in the parity checkmatrix H is set at 1, in the Tanner graph shown in FIG. 6, the ithvariable node (or the ith node marked with the “=” special character)from the top of the graph is connected by an edge to the jth check node(or the jth node marked with the “+” special character) from the top ofthe graph. An edge connecting a check node to a variable node indicatesthat a coding bit for the variable node imposes a condition ofconstraint on the check node. It is to be noted that the Tanner graphshown in FIG. 6 is a Tanner graph drawn for the parity check matrix Hshown in FIG. 5.

In accordance with a sum product algorithm adopted as an algorithm ofthe method for decoding LDPC codes, variable-node and check-nodecomputation processes are carried out repeatedly.

In a variable node, the computation according to Eq. (1) is carried outas shown in FIG. 7. That is to say, as shown in FIG. 7, a message v_(i)for an edge serving as the object of message computation is computed bymaking use of messages u₁ and u₂ from remaining edges each connected tothe variable node as well as received information u_(oi). Messages forother edges are computed in the same way.

Before the check-node computation process is explained, Eq. (2) isrewritten into Eq. (6) given below by making use of the equationa×b=exp{ ln(|a|)+ln(|b|)}×sign (a)×sign (b) where sign (x) has a valueof 1 for x≧0 and a value of −1 for x<0.

$\begin{matrix}\left\lbrack {{Eq}.\mspace{14mu} 6} \right\rbrack & \; \\{u_{j} = {{2{\tanh^{- 1}\left( {\prod\limits_{i = 1}^{d_{c} - 1}{\tanh\left( \frac{v_{i}}{2} \right)}} \right)}}\mspace{25mu} = {{2{\tanh^{- 1}\left\lbrack {\exp\left\{ {\sum\limits_{i = 1}^{d_{c} - 1}\;{\ln\left( {{\tanh\left( \frac{v_{i}}{2} \right)}} \right)}} \right\} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\mspace{14mu}\left( {\tanh\left( \frac{v_{i}}{2} \right)} \right)}}} \right\rbrack}}\mspace{25mu} = {2{\tanh^{- 1}\left\lbrack {\exp\left\{ {- \left( {\sum\limits_{i = 1}^{d_{c} - 1}{- {\ln\left( {\tanh\left( \frac{v_{i}}{2} \right)} \right)}}} \right)} \right\}} \right\rbrack} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\mspace{14mu}\left( v_{i} \right)}}}}}} & (6)\end{matrix}$

In addition, if the equation φ(x)=ln(tan h(x/2)) is defined for x≧0, theequation φ⁻¹(x)=2 tan h⁻¹(e^(−x)) holds true. Thus, Eq. (6) can berewritten into Eq. (7) given as follows.

$\begin{matrix}\left\lbrack {{Eq}.\mspace{14mu} 7} \right\rbrack & \; \\{u_{j} = {{\phi^{- 1}\left( {\sum\limits_{i = 1}^{d_{c} - 1}{\phi\left( {v_{i}} \right)}} \right)} \times {\prod\limits_{i = 1}^{d_{c} - 1}{{sign}\mspace{14mu}\left( v_{i} \right)}}}} & (7)\end{matrix}$

In a check node, the computation according to Eq. (7) is carried out asshown in FIG. 8. That is to say, as shown in FIG. 8, a message u_(j) foran edge serving as the object of message computation is computed bymaking use of messages v₁, v₂, v₃, v₄ and v₅ from remaining edges eachconnected to the check node. Messages for other edges are computed inthe same way.

It is to be noted that the function φ(x) can also be expressed by theequation φ(x)=ln((e^(x)+1)/(e^(x)−1)). Thus, the equation φ(x)=φ⁻¹(x)holds true for x>0. If the functions φ(x) and φ⁻¹(x) are implemented byhardware, the functions may be realized by making use of a LUT (Look UpTable) in some cases. In these cases, the same LUT common to both thefunctions is used.

If the sum product algorithm is implemented by making use of hardware,the variable-node computation according to Eq. (1) and the check-nodecomputation according to Eq. (7) need to be carried out repeatedly bymaking use of a proper circuit scale and at a proper operatingfrequency.

First of all, the following description explains an implementationmethod adopted in a decoding process. In accordance with theimplementation method, computations at nodes are simply carried outsequentially one computation after another in order to perform adecoding process.

It is to be noted that, in this case, let a decoding process be carriedout in order to decode codes expressed by a parity check matrix H having36 (rows)×108 (columns) as shown in FIG. 9 as codes having a coding rateof ⅔ and a code length of 108. The number of matrix elements each set at1 in the parity check matrix H is 323. Thus, the number of edges in theTanner graph representing the parity check matrix H is also 323. In theparity check matrix H shown in FIG. 9, matrix elements reset to 0 areeach represented by the period “.”.

FIG. 10 is a diagram showing a decoding apparatus for carrying out aprocess of decoding LDPC codes once.

In the decoding apparatus shown in FIG. 10, for every operating clock, amessage for 1 edge is computed.

That is, the decoding apparatus shown in FIG. 10 is provided with twoedge memories 100 and 102, a check-node computer 101, a variable-nodecomputer 103, a reception memory 104 and a control section 105.

In the decoding apparatus shown in FIG. 10, message data are read outfrom the edge memory 100 or 102 sequentially one message after another.Then, a message for an edge serving as an object of message computationis computed by making use of the messages read out from the edge memory100 or 102. Subsequently, the messages computed for the edge serving asan object of message computation are stored in the edge memory 102 or100 provided at a stage following the edge memory 100 or 102respectively sequentially one message after another. In order to carryout this decoding process repeatedly, a plurality of decoding apparatuseach like the one shown in FIG. 10 as a decoding apparatus for carryingout a process of decoding LDPC codes once are connected to each other ina cascade configuration. As an alternative, the decoding apparatus shownin FIG. 10 is used repeatedly in order to carry out the decoding processrepeatedly. It is to be noted that, in the following description, as anexample, a plurality of decoding apparatus each like the one shown inFIG. 10 as a decoding apparatus for carrying out a process of decodingLDPC codes once are connected to each other in a cascade configuration.

The edge memory 100 is used for storing messages D100 each received froma variable-node computer 103 employed in a decoding apparatus providedat the immediately preceding stage not shown in the figure in an orderthe check-node computer 101 provided at the stage following the edgememory 100 reads out the messages D100. Then, at a check-nodecomputation phase, the messages D100 are read out from the edge memory100 and supplied to the edge memory 100 as messages D101 in the orderthe messages D100 were stored in the edge memory 100.

On the basis of a control signal D106 received from the control section105, the check-node computer 101 carries out the computation processaccording to Eq. (7) by making use of the messages D101 in order togenerate a message D102, and supplies the message D102 to the edgememory 102 provided at a stage immediately following the check-nodecomputer 101.

The edge memory 102 is used for storing messages D102 received from thecheck-node computer 101 provided at the immediately preceding stage inan order the variable-node computer 103 provided at the stageimmediately following the edge memory 102 reads out the messages D100.Then, at a variable-node computation phase, the messages D102 are readout from the edge memory 102 and supplied to the variable-node computer103 as messages D103 in the order the messages D102 were stored in theedge memory 102.

In addition, the variable-node computer 103 also receives a controlsignal D107 from the control section 105 and received data D104 from thereception memory 104. On the basis of the control signal D107, thevariable-node computer 103 carries out the computation process accordingto Eq. (1) by making use of the message D103 received from the edgememory 100 and the received data D104 received from the reception memory100 in order to produce a message D105 as a result of the computationprocess, and supplies the message D105 to an edge memory 100 employed ina decoding apparatus provided at the immediately following stage notshown in the figure.

The reception memory 104 is used for storing LDPC codes, which arereceived data already converted into LDPC codes. The control section 105supplies the control signal D106 to the check-node computer 101 as asignal for controlling the check-node computation process. By the sametoken, the control section 105 supplies the control signal D107 to thevariable-node computer 103 as a signal for controlling the variable-nodecomputation process. The control section 105 supplies the control signalD106 to the check-node computer 101 when messages received from alledges have been stored in the edge memory 100. By the same token, thecontrol section 105 supplies the control signal D107 to thevariable-node computer 103 when messages received from all edges havebeen stored in the edge memory 102.

FIG. 11 is a block diagram showing a typical configuration of thecheck-node computer 101 employed in the decoding apparatus shown in FIG.10 as a check-node computer 101 for carrying out check-node computationprocesses sequentially one process after another.

It is to be noted that, in the configuration shown in FIG. 11 as theconfiguration of the check-node computer 101, each message is quantizedinto a total of 6 bits including a sign bit. In addition, in theconfiguration shown in FIG. 11, a check-node computation process iscarried out on LDPC codes defined by the parity check matrix H shown inFIG. 9. Moreover, the check-node computer 101 shown in FIG. 11 receivesa clock signal ck providing the necessary clock signal ck to thecheck-node computer 101. Thus, each block employed in the check-nodecomputer 101 carries out an operation synchronously with the clocksignal ck.

On the basis of the control signal D106 received from the controlsection 105 as a control signal including typically 1 bit, thecheck-node computer 101 shown in FIG. 11 carries out the computationprocess according to Eq. (7) by making use of messages D101 sequentiallyread out from the edge memory 100 one message after another.

That is to say, the check-node computer 101 reads out 6-bit messagesD101 (or messages v_(i)) each received from a variable nodecorresponding to a column of the parity check matrix H sequentially onemessage after another, supplying the less significant bits included inthe message as bits representing an absolute value D122 (|v_(i)|) of themessage to a LUT 121 and the most significant bit D121 included in themessage as a bit representing the sign of the message to an EXOR circuit129 and a FIFO (First In First Out) memory 133. In the check-nodecomputer 101, the control signal D106 received from the control section105 is supplied to selectors 124 and 131.

For the absolute value D122 (|v_(i)|) supplied to the LUT 121, the LUT121 reads out 5-bit data D123 (φ(|v_(i)|) used in the computationprocess according to Eq. (7)) and supplies the data D123 (φ(|v_(i)|)) toan adder 122 and a FIFO memory 127.

The adder 122 adds the data D123 (φ(|v_(i)|)) to 9-bit data D124 storedin a register 123 and stores back the cumulative sum including 9 bits inthe register 123 as new 9-bit data D124 replacing the previous data D124also including 9 bits. It is to be noted that, when the process to findthe cumulative sum has been completed for the absolute values D122(|v_(i)|) of messages D101 received from all the edges along 1 row ofthe parity check matrix H, the register 123 is reset.

When messages D101 received from all the edges along 1 row of the paritycheck matrix H are read out sequentially one message after another andthe final cumulative sum representing the sum of function values D123along the row is stored in the register 123, the control section 105changes the control signal D106 supplied thereby from 0 to 1. For a rowweight of 9 for example, the control signal D106 stays at 0 during aperiod covering the first to eighth clock pulses. As the ninth clockpulse is generated, the control section 105 changes the control signalD106 from 0 to 1.

With the control signal D106 set at 1, a selector 124 selects thecumulative sum D124 stored in the register 123 and supplies thecumulative sum D124 to a register 125 as data D125 to be stored in theregister 125. The cumulative sum D124 stored in the register 123 withthe control signal D106 set at 1 is a 9-bit value obtained as a resultof cumulatively adding the function values D123 (or φ(|v_(i)|)) obtainedfor messages D101 (or messages v_(i)) received from all the edges along1 row of the parity check matrix H. That is to say, the cumulative sumD124 stored in the register 123 with the control signal D106 set at 1 isthe value of Σφ(|v_(i)|) for a summation range starting from i=1 andending at i=d_(c). The data D125 stored in the register 125 is suppliedto the selector 124 and an adder 126 as data D126 including 9 bits. Withthe control signal D106 reset at 0, on the other hand, the selector 124selects the 9-bit data D126 received from the register 125 and outputsthe selected data D126 including 9 bits to the register 125 as data tobe stored in the register 125 again. That is to say, the register 125supplies a cumulative value obtained previously as the 9-bit cumulativesum of the function values φ(|v_(i)|) to the selector 124 and the adder126 till data including 9 bits is obtained as a result of cumulativelyadding the function values φ(|v_(i)|) obtained for messages D101 (ormessages vi) received from all the edges along 1 row of the parity checkmatrix H.

On the other hand, the FIFO memory 127 delays the data D123 (φ(|v_(i)|))output by the LUT 121 to a point of time at which the register 125supplies new data D126 (Σφ(|v_(i)|) for a summation range starting fromi=1 and ending at i=d_(c)) to the adder 126. Then, the FIFO memory 127supplies the data D123 to an adder 126 as data D127 including 5 bits.The adder 126 subtracts the data D127 supplied by the FIFO memory 127from the data D126 supplied by the register 125 and supplies thedifference to an LUT 128 as difference data D128 including 5 bits. Thatis to say, the adder 126 subtracts the 5-bit function value φ(|v_(i)|)found for a message D101 (or a message v_(i)) received from an edgeserving as an object of message computation from 9-bit data obtained asa result of cumulatively adding the function values φ(|v_(i)|) obtainedfor messages D101 (or messages v_(i)) received from all the edges along1 row of the parity check matrix H, and supplies the difference to anLUT 128 as the difference data D128 including 5 bits. The differencedata D128 is thus the value of Σφ(|v_(i)|) for a summation rangestarting from i=1 and ending at i=(d_(c)−1).

It is to be noted that, even though the adder 126 subtracts the 5-bitdata D127 supplied by the FIFO memory 127 from the 9-bit data D126supplied by the register 125 to result in a difference including up to 9bits, the adder 126 supplies difference data D128 including 5 bits. Inconsequence, if the adder 126 subtracts the 5-bit data D127 supplied bythe FIFO memory 127 from the 9-bit data D126 supplied by the register125 to result in a difference, that cannot be expressed by 5 bits, thatis, if the adder 126 produces a difference greater than 31 (or 11111 ifrepresented in the binary format), which is the maximum value of dataincluding 5 bits, the adder 126 clips the difference to the maximumvalue of 31 and supplies the maximum value as the difference data D128including 5 bits.

For the difference data D128, which is the value of Σφ(|v_(i)|) for asummation range starting from i=1 and ending at i=(d_(c)−1), the LUT 128reads out 5-bit data D129 (φ⁻¹(Σφ(|v_(i)|)) used in the computationprocess according to Eq. (7)).

Concurrently with the processing described above, the EXOR circuit 129computes the exclusive logical sum of 1-bit data D131 stored in aregister 130 and the sign bit D121. That is to say, the EXOR circuit 129computes the product of two sign bits. The multiplication result D130including 1 bit is stored back in the register 130. It is to be notedthat, when the sign bits D121 extracted from messages D101 received fromall the edges along 1 row of the parity check matrix H have beensubjected to the multiplication process carried out by the EXOR circuit129, the contents of the register 130 are reset.

When the multiplication result D130 (Πsign (v_(i)) from i=1 and endingat i=d_(c)) obtained from the multiplication processes carried out onthe sign bits D121 extracted from messages D101 received from all theedges along 1 row of the parity check matrix H is stored in the register130, the control section 105 changes the control signal D106 suppliedthereby from 1 to 0.

With the control signal D106 set at 1, a selector 131 selects themultiplication result D131 stored in the register 130 and supplies themultiplication result D131 to a register 132 as 1-bit data 132 to bestored in the register 132. As described above, the multiplicationresult D131 stored in the register 130 with the control signal D106 setat 1 is a 1-bit data obtained as a result of the multiplicationprocesses on the sign bits D121 extracted from messages D101 receivedfrom all the edges along 1 row of the parity check matrix H. That is tosay, the multiplication result D131 stored in the register 130 with thecontrol signal D106 set at 1 is the value of Π sign (v_(i)) for amultiplication range starting from i=1 and ending at i=d_(c). The dataD132 stored in the register 132 is supplied to the selector 131 and anEXOR circuit 134 as data D133 including 1 bit. With the control signalD106 reset at 0, on the other hand, the selector 131 selects the 1-bitdata D133 received from the register 132 and outputs the selected dataD133 including 1 bit to the register 132 as data to be stored in theregister 132 again. That is to say, the register 132 supplies the dataD133 already stored therein to the EXOR circuit 134 and the selector 131till data including 1 bit is obtained as a result of the multiplicationprocesses carried out by the EXOR circuit 129 on the sign bits D121extracted from messages D101 (or messages v_(i)) received from all theedges along 1 row of the parity check matrix H.

On the other hand, the FIFO memory 133 delays the sign bit D121 to apoint of time at which the register 132 supplies new data D133 (or thevalue of Π sign (v_(i)) for a multiplication range starting from i=1 andending at i=d_(c)) to the EXOR circuit 134. Then, the FIFO memory 133supplies the delayed sign bit D121 to the EXOR circuit 134 as data D134including 1 bit. The EXOR circuit 134 computes an exclusive logical sumof the data D133 received from the register 132 and the 1-bit data D134received from the FIFO memory 133 in order to divide the data D133 bythe data D134 including 1 bit, producing a division result alsoincluding 1 bit. Then, the EXOR circuit 134 outputs the division resultincluding 1 bit as data D135. That is to say, the EXOR circuit 134divides a product of sign bits D121 (sign (|v_(i)|)) extracted frommessages D101 received from all the edges along 1 row of the paritycheck matrix H by the sign bit D121 (sign (|v_(i)|)) extracted from amessage D101 (or a message v_(i)) received from an edge serving as anobject of message computation, and outputs the division result (or thevalue of Π sign (v_(i)) for a multiplication range starting from i=1 andending at i=(d_(c)−1)) as the division result D135.

The check-node computer 101 concatenates the 5-bit processing resultD129 generated by the LUT 128 with the 1-bit division result D135produced by the EXOR circuit 134 by taking the processing result D129including 5 bits as 5 less significant bits and the division result D135including 1 bit as the most significant bit in order to output a messageD102 (or a message u_(j)) including a total of 6 bits.

As described above, the check-node computer 101 carries out thecomputation processing according to Eq. (7) in order to find a messageu_(j).

It is to be noted that, since the maximum value of the row weight forthe parity check matrix H shown in FIG. 9 is nine, that is, since themaximum number of messages supplied to the check node is nine, thecheck-node computer 101 is provided with the FIFO memory 127 and theFIFO memory 133, which are used for delaying the nine messages (or thevalue of the function φ(|v_(i)|)). In a process to handle row messagesfewer than the row weight of 9, the magnitude of the delay provided bythe FIFO memory 127 and the FIFO memory 133 can be reduced to a valuecorresponding to the row weight for the processed row messages.

FIG. 12 is a block diagram showing a typical configuration of thevariable-node computer 103 included in the decoding apparatus shown inFIG. 10 as a variable-node computer 103 for carrying out variable-nodecomputation processes sequentially one process after another.

It is to be noted that, in the configuration shown in FIG. 12 as atypical configuration of the variable-node computer 103, each message isquantized into a total of 6 bits including a sign bit. In addition, inthe configuration shown in FIG. 12, a variable-node computation processis carried out on LDPC codes expressed by the parity check matrix Hshown in FIG. 9. On top of that, the variable-node computer 103 shown inFIG. 12 receives a clock signal ck providing the necessary clock signalck to the variable-node computer 103. Thus, each block employed in thevariable-node computer 103 carries out an operation synchronously withthe clock signal ck.

On the basis of the control signal D107 received from the controlsection 105 as a control signal having typically 1 bit, thevariable-node computer 103 shown in FIG. 12 carries out the computationprocess according to Eq. (1) by making use of messages D103 sequentiallyread out from the edge memory 102 one message after another and receiveddata D104 read out from the reception memory 104.

That is to say, the variable-node computer 103 reads out 6-bit messagesD103 (or messages uj) each received from a check node corresponding to arow of the parity check matrix H sequentially one message after another,supplying the messages D103 to an adder 151 and a FIFO memory 155. Inaddition, the variable-node computer 103 reads out pieces of receivedD104 including 6 bits from the reception memory 104 sequentially onepiece after another, supplying the pieces of received including 6 bitsto an adder 156. The variable-node computer 103 supplies a controlsignal D107 received from the control section 105 to a selector 153.

The adder 151 adds the message D103 (or the message u_(j)) to 9-bit dataD151 stored in a register 152 in order to produce a cumulative messageD103 including 9 bits and stores the cumulative message D103 alsoincluding 9 bits also in the register 152. It is to be noted that, afterthe messages D103 received from all the edges along one column of theparity check matrix H are cumulatively added and stored in the register152, the contents of the register 152 are reset.

After the variable-node computer 103 reads out messages D103 receivedfrom all edges along a column of the parity check matrix H sequentiallyone message after another and the adder 151 adds the message D103 inorder to produce a cumulative message D103 including 9 bits and storesthe cumulative message D103 also including 9 bits also in the register152, the control section 105 changes the control signal D107 suppliedthereby from 0 to 1. In the case of a column weight of 5 for example,the control signal D107 stays at 0 during a period covering the first tofourth clock pulses. As the fifth clock pulse is generated, the controlsection 105 changes the control signal D107 from 0 to 1.

With the control signal D107 set at 1, a selector 153 selects the 9-bitcumulative sum D151 stored in the register 152 and supplies the selectedcumulative sum D151 to a register 154 to be stored in the register 154.The cumulative sum D151 stored in the register 152 set at 1 is a 9-bitvalue obtained as a result of cumulatively adding the messages D103 (ormessages u_(j)) received from all the edges along 1 column of the paritycheck matrix H. That is to say, the cumulative sum D151 stored in theregister 152 set at 1 is the value of Σu_(j) for a summation rangestarting from j=1 and ending at j=d_(v). The data D151 stored in theregister 154 is supplied to the selector 153 and an adder 156 as dataD152 consisting of 9 bits. With the control signal D107 reset at 0, onthe other hand, the selector 153 selects the 9-bit data D152 receivedfrom the register 154 and outputs the selected data D152 including 9bits to the register 154 as data to be stored in the register 154 again.That is to say, the register 154 supplies the 9-bit data D152 obtainedas a result of the cumulative additions carried out previously to theselector 153 and the adder 156 till data consisting of 9 bits isobtained as a result of cumulatively adding the function valuesφ(|v_(i)|) obtained for messages D103 (or messages u_(j)) received fromall the edges along 1 column of the parity check matrix H.

On the other hand, a FIFO memory 155 delays the message D103 receivedfrom a check node to a point of time at which the register 154 suppliesnew data D152 (Σu_(j) for a summation range starting from i=1 and endingat i=d_(v)) to an adder 156. Then, the FIFO memory 155 supplies thedelayed data D103 to the adder 156 as data D153 including 6 bits. Theadder 156 subtracts the data D153 supplied by the FIFO memory 155 fromthe data D152 supplied by the register 154. That is to say, the adder156 subtracts the message u_(j) received from an edge serving as anobject of message computation from the messages D103 (the messagesu_(j)) received from all the edges along 1 column of the parity checkmatrix H, and outputs the difference. The difference is thus the valueof Σu_(j) for a summation range starting from j=1 and ending atj=(d_(v)−1). In addition, the adder 156 adds the difference (which isthe value of Σu_(j) for a summation range starting from j=1 and endingat j=(d_(v)−1)) to the received data D104 read out from the receptionmemory 104 in order to produce a sum including 6 bits and outputs thesum as a message D105 (a message v_(i)).

As described above, the variable-node computer 103 carries out acomputation process according to Eq. (1) in order to generate a messagev_(i).

It is to be noted that, since the maximum value of the column weight forthe parity check matrix H shown in FIG. 9 is 5, that is, since themaximum number of messages supplied to the variable node is 5, thevariable-node computer 1031 s provided with the FIFO memory 155 fordelaying the five messages u_(j). In a process to handle column messagesfewer than the column weight of 5, the magnitude of the delay providedby the FIFO memory 155 can be reduced to a value corresponding to acolumn weight for the processed column messages.

As described above, the adder 156 subtracts the 6-bit data D153 suppliedby the FIFO memory 155 from the 9-bit data D152 supplied by the register154, producing a difference and, then, the adder 156 adds the differenceto the 6-bit received data D104 read out from the reception memory 104in order to produce a result smaller than a minimum value, which can berepresented by a message D105 including 6 bits, or a result greater thana maximum value. If the adder 156 produces a result smaller than theminimum value, which can be represented by a message D105 including 6bits, the adder 156 clips the result to the minimum value. If the adder156 produces a result greater than the maximum value, which can berepresented by a message D105 including 6 bits, on the other hand, theadder 156 clips the result to the maximum value.

The decoding apparatus shown in FIG. 10 receives control signals fromthe control section 105 in accordance with weights of the parity checkmatrix H. Then, by merely changing the control signals, the decodingapparatus is capable of decoding LDPC codes by making use of variousparity check matrixes H provided that the storage capacities of the edgememory 100, the edge memory 102, the FIFO memory 127 and the FIFO memory133, which are employed in the check-node computer 101, and the FIFOmemory 155 employed in the variable-node computer 103 are sufficient.

It is to be noted that, at the last decoding stage in the decodingapparatus shown in FIG. 10, a process according to Eq. (5) can becarried out as a substitute for the variable-node process according toEq. (1) and the result of the process according to Eq. (5) can be outputas the final decoding result. This feature is not shown in the figurethough.

If the LDPC codes are decoded by making use of a series of decodingapparatus each like the one shown in FIG. 10, the check-node processingand the variable-node processing are carried out alternately. That is tosay, in such a series of decoding apparatus each like the one shown inFIG. 10, a variable-node computer 103 carries out the variable-nodeprocessing by making use of the result of the check-node processingcarried out by a check-node computer 101 whereas a check-node computer101 carries out the check-node processing by making use of the result ofthe variable-node processing carried out by a variable-node computer103.

Thus, in a decoding process making use of a parity check matrix H having323 edges as shown in FIG. 9, 646 (=323×2) clock pulses are required. Inorder to carry out 50 decoding processes for example, 108 codes formingreceived data are handled as a frame. In this case, the number 108 isthe code length. While 1 frame is being received, an operation driven by32,300 (=646×50) clock pulses is necessary. That is to say, an operationof a high speed about 300 (≈32,300/108) times the receiving frequency isnecessary. If the receiving frequency is several tens of MHz, anoperation of a high speed of at least 1 GHz is necessary.

In a process to decode LDPC codes by making use a series of 50interconnected decoding apparatus each like the one shown in FIG. 10 forexample, while a variable-node computer is carrying out a variable-nodeprocess on a first frame, a check-node computer carries out a check-nodeprocess on a second frame and another variable-node computer carries outa variable-node process on a third frame and so on. In this way, aplurality of variable-node processes and a plurality of check-nodeprocesses can be carried out at the same time. In this case, it isnecessary only to carry out computations on 323 edges while 108 codesare being received. Thus, the decoding apparatus only needs to carry outan operation of a high speed equivalent to about 3 (≈323/108) times thereceiving frequency, and such an operation can be well implemented. Inthis case, however, simple estimation indicates that the circuit scaleis 50 times the size of the decoding apparatus shown in FIG. 10.

The following description explains a method for implementing a decodingapparatus having a full parallel decoding configuration in whichprocesses of all node are carried out at the same time.

This method for implementing a decoding apparatus having a full paralleldecoding configuration is described in documents such as Non-PatentDocument 1.

FIG. 13 is a block diagram showing a typical configuration of a decodingapparatus for decoding codes expressed by the parity check matrix Hshown in FIG. 9 as codes having a coding rate of ⅔ and a code length of108.

In the decoding apparatus shown in FIG. 13, all messages received from323 edges are read out from an edge memory 202 or 206 at the same timeand used for generating new messages for the 323 edges. Then, theresulting new messages are stored at the same time respectively in theedge memory 206 or 202 provided at the following stage. Thus, the LDPCcodes can be decoded by making use of a series of decoding apparatuseach like the one shown in FIG. 13.

The decoding apparatus shown in FIG. 13 includes a reception memory 205,two edge reshuffling devices 200 and 203, the two edge memories 202 and206 mentioned above, 36 check-node computers 201 ₁ to 201 ₃₆ and 108variable-node computers 204 ₁ to 204 ₁₀₈. These memories, sections andcomputers are explained in detail as follows.

The edge memory 206 is used for storing all messages D206 ₁ to D206 ₁₀₈received from respectively variable-node computers 204 ₁ to 204 ₁₀₈provided at the immediately preceding stage at the same time. Then, atthe next time (or the next clock timing), the messages D206 ₁ to D206₁₀₈ are read out as respectively messages D207 ₁ to D207 ₁₀₈, which aresupplied to an edge reshuffling device 200 provided at the Immediatelysucceeding stage as messages D200 (strictly speaking, messages D200 ₁ toD200 ₁₀₈ respectively). The edge reshuffling device 200 rearranges theorder of the messages D200 ₁ to D200 ₁₀₈ received from the edge memory206 in accordance with the parity check matrix H shown in FIG. 9 andsupplies the rearranged messages to the check-node computers 201 ₁ to201 ₃₆ as messages D201 ₁ to D201 ₃₆.

The check-node computers 201 ₁ to 201 ₃₆ carry out the computationprocess according to Eq. (7) on respectively the messages D201 ₁ to D201₃₆ received from the edge reshuffling device 200 in order to producemessages D202 ₁ to D202 ₃₆ respectively as a result of the computationprocess and supplies the messages D202 ₁ to D202 ₃₆ to the edge memory202.

The edge memory 202 is used for storing all the messages D202 ₁ to D202₃₆ from the check-node computers 201 ₁ to 201 ₃₆ respectively at thesame time. Then, at the next time, the messages D202 ₁ to D202 ₃₆ areread out from the edge memory 202 as respectively messages D203 ₁ toD203 ₃₆, which are supplied to an edge reshuffling device 203 providedat the immediately succeeding stage.

The edge reshuffling device 203 rearranges the order of the messagesD203 ₁ to D203 ₃₆ received from the edge memory 202 in accordance withthe parity check matrix H shown in FIG. 9 and supplies the rearrangedmessages to the variable-node computers 204 ₁ to 204 ₁₀₈ as messagesD204 ₁ to D204 ₁₀₈.

The variable-node computers 204 ₁ to 204 ₁₀₈ carry out the computationprocess according to Eq. (1) on the messages D204 ₁ to D204 ₁₀₈ receivedfrom the edge reshuffling device 203 and the messages D205 ₁ to D205 ₁₀₈received from the reception memory 205 in order to produce messages D206₁ to D206 ₁₀₈ respectively as a result of the computation process andsupplies the messages D206 ₁ to D206 ₁₀₈ to the edge memory 206 providedat the immediately succeeding state.

FIG. 14 is a diagram showing a typical configuration of each of thecheck-node computers 201 _(m) (where m=1, 2, . . . 36) employed in thedecoding apparatus shown in FIG. 13 as computers for carrying outcheck-node processes at the same time.

A check-node computer 201 m shown in FIG. 14 carries out a check-nodeprocess according to Eq. (7) in the same way as the check-node computer101 shown in FIG. 11. Check-node processes are, however, carried out atthe same time on all edges.

That is to say, in the check-node computer 201 _(m) shown in FIG. 14,messages D221 ₁ to D221 ₉ (messages v_(i)) originally received fromvariable nodes each corresponding to a row of the parity check matrix Hshown in FIG. 9 are all acquired at the same time from the edgereshuffling device 200. The 5 less significant bits of each of themessages D222 ₁ to D222 ₉ (v_(i)) are the absolute value (|v_(i)|) ofeach of the messages D222 ₁ D222 ₉ (v_(i)) respectively, the absolutevalues (|v_(i)|) being supplied to LUTs 221 ₁ to 221 ₉ respectively. Onthe other hand, the most significant bit of each of the messages D221 ₁to D221 ₉ (v_(i)) are the sign of each of the messages D221 ₁ D221 ₉(v_(i)) respectively. The signs denoted by notations D223 ₁ to D223 ₉are supplied to EXOR circuits 226 ₁ to 226 ₉ respectively and an EXORcircuit 225.

For the absolute value D222 ₁ to D222 ₁ (|v_(i)|), the LUT 221 ₁ to LUT221 ₉ reads out 5-bit data D224 ₁ to D224 ₉ (or the 5-bit value of thefunction (φ(|v_(i)|) used in the computation process according to Eq.(7)) and supplies computation results D224 ₁ to D224 ₉ (φ(|v_(i)|)) to asubtractor 223 ₁ to 223 ₉ and an adder 222.

The adder 222 finds a 9-bit sum D225 of the computation results D224 ₁to D224 ₉. The sum D225 including 9 bits is the sum of computationresults D224 ₁ to D224 ₉ obtained for 1 row of the parity check matrixH. That is to say, the sum D225 consisting of 9 bits is the value ofΣφ(|v_(i)|) for a summation range starting from i=1 and ending at i=9.The adder 222 supplies the sum D225 including of 9 bits to thesubtractors 223 ₁ to 223 ₉. The subtractors 223 ₁ to 223 ₉ subtract thecomputation results D224 ₁ to D224 ₉ (or the values of the functionφ(|v_(i)|)) from the sum D225 to give differences D227 ₁ to D227 ₉ eachincluding 5 bits and supplies to LUT 224 ₁ to 224 ₉. That is to say, thesubtractors 223 ₁ to 223 ₉ subtract the value of the function φ(|v_(i)|)obtained for a message v_(i) received from an edge serving as an objectof message computation from the sum of the values of the functionφ(|v_(i)|) obtained for messages v_(i) received from all edges andoutputs the differences D227 ₁ to D227 ₉ each including 5 bits to theLUT 224 ₁ to 224 ₉ respectively. Thus, the differences D227 ₁ to D227 ₉each including 5 bits are each the value of Σφ(|v_(i)|) for a summationrange starting from i=1 and ending at i=8. For the differences D227 ₁ toD227 ₉ each including 5 bits respectively, the LUTs 224 ₁ to 224 ₉ readout respectively 5-bit data D228 ₁ to 228 ₉ (or the 5-bit values of thefunction φ⁻¹ (Σφ(|v_(i)|)) used in the computation process according toEq. (7)).

On the other hand, an EXOR circuit 225 computes the exclusive logicalsum of all the sign bits D223 ₁ to D223 ₉ in order to find a 1-bitproduct D226 of all the sign bits D223 ₁ to D223 ₉. Then, the EXORcircuit 225 outputs the product D226 including 1 bit to EXOR circuits226 ₁ to 226 ₉. The product D226 including 1 bit is the value of Π sign(v_(i)) for a multiplication range starting from i=1 and ending at i=9.The EXOR circuits 226 ₁ to 226 ₉ find the exclusive logical sum of theproduct D226 including 1 bit and the sign bits D223 ₁ to D223 ₉respectively in order to divide the sign bits D223 ₁ to D223 ₉ by theproduct D226 including 1 bit to give division results D229 ₁ to D229 ₉,which are each the value of Π sign (v_(i)) for a multiplication rangestarting from i=1 and ending at i=8.

A check-node computer 201 _(m) outputs messages D230 ₁ to D230 ₉ as aresult of the check-node process carried out thereby. The messages D230₁ to D230 ₉ are each message including a total of 6 bits. The 5 lesssignificant bits of each of the messages D230 ₁ to D230 ₉ are one of the5-bit processing results D228 ₁ to D228 ₉ output by the LUT 224 ₁ to 224₉ respectively. On the other hand, the most significant bit of each ofthe messages D230 ₁ to D230 ₉ is one of the division results D229 ₁ toD229 ₉ output by the EXOR circuits 226 ₁ to 226 ₉ respectively.

As described above, a check-node computer 201 _(m) carries out acheck-node process according to Eq. (7) in order to find a messageu_(j).

It is to be noted that, in the configuration shown in FIG. 14 as theconfiguration of a check-node computer 201 _(m), each message isquantized into a total of 6 bits including a sign bit. In addition, thecircuit shown in FIG. 14 as the circuit of a check-node computercorresponds to 1 check node. There are as many check nodes as rows ofthe parity check matrix H shown in FIG. 9 as a parity check matrix Hserving as the object of the check-node process. Since the parity checkmatrix H has 36 rows as shown in FIG. 9, the decoding apparatus shown inFIG. 13 includes 36 check-node computers 201 _(m) each like the oneshown in FIG. 14.

As described above, the check-node computer 201 _(m) shown in FIG. 14 iscapable of computing nine messages at the same time. In addition, sincethe row weights of the parity check matrix H shown in FIG. 9 as a paritycheck matrix serving as the object of the check-node process are 8 forthe first row and 9 for each of the second to thirty-sixth rows, that isto say, since the number of messages supplied to the check node is 8 for1 check-node computer 201 _(m) corresponding to the first row having arow weight of 8, or is 9 for 35 check-node computers 201 _(m)respectively corresponding to the second to thirty-sixth rows eachhaving a row weight of 9, the check-node computer 201 _(m) has aconfiguration capable of computing 8 messages at the same time in thesame way as the circuit shown in FIG. 14 whereas each of the remaining35 check-node computers 201 ₂ to 201 ₃₆ has the same configuration asthe circuit shown in FIG. 14 and is hence capable of computing 8messages at the same time in the same way as the circuit shown in FIG.14.

FIG. 15 is a diagram showing a typical configuration of each of thevariable-node computers 204 _(p) (where p=1, 2, . . . 108) employed inthe decoding apparatus shown in FIG. 13 as computers for carrying outcheck-node processes at the same time.

A check-node computer 204 _(p) shown in FIG. 15 carries out avariable-node process according to Eq. (1) in the same way as thevariable-node computer 103 shown in FIG. 12. Variable-node processesare, however, carried out at the same time on all edges.

That is to say, in the variable-node computer 204 _(p) shown in FIG. 15,the 6-bit messages D251 ₁ to D251 ₅ (messages u_(j)) received from checknodes each corresponding to a row of the parity check matrix H are allacquired at the same time from the edge reshuffling device 203. The6-bit messages D251 ₁ to D251 ₅ (or messages u_(j)) are supplied toadders 252 ₁ to 252 ₅ and an adder 251. In addition, the variable-nodecomputer 204 _(p) also receives received data D271 from the receptionmemory 205. The received data D271 is then supplied to the adders 252 ₁to 252 ₅.

The adder 251 computes a sum D252 including 9 bits as the sum of all the6-bit messages D251 ₁ to D251 ₅ (or messages u_(j)) and outputs the sumD252 including 9 bits to the adders 252 ₁ to 252 ₅. The sum D252including 9 bits is the value of Σu_(j) for a summation range startingfrom j=1 and ending at j=5. The adders 252 ₁ to 252 ₅ subtract the 6-bitmessages D251 ₁ to D251 ₅ (or messages u_(j)) respectively from the sumD252. The 6-bit messages D251 ₁ to D251 ₅ (or messages u_(j)) subtractedby the adders 252 ₁ to 252 ₅ respectively from the sum D252 are each amessage received from an edge serving as an object of messagecomputation whereas the sum D252 is a result computed from messagesu_(j) received from all edges. Thus, the differences obtained as resultsof subtracting the 6-bit messages D251 ₁ to D251 ₅ (or messages u_(j))respectively from the sum D252 are each the value of Σu_(j) for asummation range starting from j=1 and ending at j=4.

In addition, the adders 252 ₁ to 252 ₅ add received data D271 (u_(oi))to the subtracting values (or the values of Σu_(j) for a summation rangestarting from j=1 and ending at j=4) to give 6-bit sums D253 ₁ to D253₅, which are each output as a result of the variable-node process.

As described above, the variable-node computer 204 _(p) carries out avariable-node process according to Eq. (1) in order to generate messagesv_(i).

It is to be noted that, in the configuration shown in FIG. 15 as theconfiguration of a variable-node computer 204 _(p), each message isquantized into a total of 6 bits including a sign bit. In addition, thecircuit shown in FIG. 15 corresponds to 1 variable node. There are asmany variable nodes as columns of the parity check matrix H shown inFIG. 9 as a parity check matrix H serving as the object of thevariable-node process. Since the parity check matrix H has 108 columnsas shown in FIG. 9, the decoding apparatus shown in FIG. 13 includes 108circuits like the one shown in FIG. 15.

Thus, the variable-node computer 204 _(p) shown in FIG. 15 is capable ofcomputing five messages at the same time. Since the parity check matrixH shown in FIG. 9 as a parity check matrix serving as the object of thevariable-node process has column weights of 5, 3, 2 and 1 on 18, 54, 35and 1 columns respectively, 18 of the 108 variable-node computers 204 ₁to 204 ₁₀₈ corresponding respectively to 18 columns each having a columnweight of 5 each have the same configuration as the circuit shown inFIG. 15. The remaining 54, 35, 1 variable-node computers 204 _(p)corresponding respectively to 54, 35, 1 columns each having a columnweight of 3, 2, 1 are each capable of computing 3, 2. 1 messages at thesame time in the same way as the circuit shown in FIG. 15.

It is to be noted that, at the last decoding stage in the decodingapparatus shown in FIG. 13, a process according to Eq. (5) can becarried out as a substitute for the variable-node process according toEq. (1) and the result of the process according to Eq. (5) can be outputas the final decoding result as is the case with the decoding apparatusshown in FIG. 10. This feature is not shown in the figure though.

As described above, the decoding apparatus shown in FIG. 13 is capableof computing all messages received from 323 edges at the same time in 1clock.

If LDPC codes are decoded by making use of a series of decodingapparatus each like the one shown in FIG. 13, the check-node processingand the variable-node processing are carried out alternately and ittakes time of two clocks to complete one decoding process. Thus, if itis necessary to carry out 50 decoding processes, only 100 (2×50) clockoperations need to be performed while receiving received data takingcodes with a code length of 108 as 1 frame. As a result, the operatingfrequency is about equal to the receiving frequency. In general, theLDPC codes have a large code length in a range of several thousands toseveral tens of thousands. By using the decoding apparatus shown in FIG.13, it is possible to set a very large number as the number of times thedecoding processing is to be carried out. Therefore, improvement of theerror correction performance can be expected.

Since the decoding apparatus shown in FIG. 13 computes messagescorresponding to all edges of the Tanner graph concurrently, however,the circuit scale of the decoding apparatus increases proportionally tothe code length. In addition, if the decoding apparatus shown in FIG. 13is designed as an apparatus for decoding the LDPC codes defined by aparity check matrix H as codes having a certain code length and acertain coding rate, it will be difficult to decode LDPC codes expressedby a parity check matrix H other than the certain parity check matrix Has codes having a code length other than the certain code length and acoding rate other than the certain coding rate. That is to say, it isdifficult to apply the decoding apparatus shown in FIG. 13 to a case inwhich a variety of codes can be decoded by merely changing controlsignals as is the case with the decoding apparatus shown in FIG. 10. Inother words, the decoding apparatus shown in FIG. 13 exhibits much codedependence.

In addition to the decoding methods adopted by the decoding apparatusshown in FIGS. 10 and 13, there is a decoding method described indocuments such as Non-Patent Document 2 as a decoding method fordecoding neither one message at one time nor all messages at the sametime, that is, as a decoding method for decoding four messages at onetime. The decoding method described in Non-Patent Document 2 has aproblem that, in general, it is not easy to avoid operations to read outdata from different addresses in a memory at the same time andoperations to write data into different addresses in the memory at thesame time. That is to say, it is hard to control accesses to the memory.

In order to solve the problem described above, there has been reported acoding and decoding apparatus (for example, referred to as Non-PatentDocuments 3 and 4) as an apparatus much suitable for implementation of adecoder for decoding partially parallel codes instead of decoding randomcodes. However, a method for implementing the decoding apparatusdescribed in Non-Patent Document 3 is a method devised for specificcodes. With this method, it is thus difficult to decode codes having avariety of code lengths and a variety of coding rates.

Documents such as Patent Document 1 describe a decoding apparatuscapable of decoding codes having a variety of code lengths and a varietyof coding rates if the codes are LDPC codes expressed by a parity checkmatrix H like one shown in FIG. 16. As shown in the figure, the paritycheck matrix H is a matrix that can be represented as a combination of6×6 unit matrixes, a matrix obtained by setting one or more of the “1”elements of a unit matrix to 0 (hereinafter referred to as semi unitmatrixes accordingly), a matrix obtained by carrying out a cyclic shiftoperation on a unit matrix or a semi unit matrix (hereinafter referredto as shift matrixes accordingly), a matrix obtained by computing thesum of at least any two of a unit matrix, a semi unit matrix and a shiftmatrix (or the sum of a plurality such matrixes)(hereinafter referred toas sum matrixes accordingly) and 0 matrixes including a 6×6 matrix eachhaving all elements thereof set to 0. The decoding apparatus is alsocapable of decoding codes having a variety of code lengths and a varietyof coding rates if the codes are LDPC codes according to the transposedmatrix of the parity check matrix H shown in FIG. 16 as a matrix thatcan be expressed as a combination of the these matrixes.

It is to be noted that the parity check matrix H shown in FIG. 16 isobtained by providing a gap between any two adjacent 6×6 matrixesincluded in the parity check matrix H shown in FIG. 9. In the followingdescription, the unit matrix, the semi unit matrix, the shift matrix,the sum matrix and the 0 matrix, which are combined to form the paritycheck matrix H shown in FIG. 16, are each properly referred to as acomponent matrix.

By referring to FIGS. 17 to 22, the following description explains adecoding apparatus for decoding LDPC codes that can be expressed by theparity check matrix H shown in FIG. 16.

FIG. 17 is a block diagram showing a typical configuration of a decodingapparatus 400 for decoding LDPC codes that can be expressed by theparity check matrix H shown in FIG. 16.

The decoding apparatus 400 employs a decoding intermediate resultstorage memory 410, a cyclic shift circuit 411, a computation section412 having six computers 412 ₁ to 412 ₆, a decoding intermediate resultstorage memory 413, a cyclic shift circuit 414, a computation section415 having six computers 415 ₁ to 415 ₆, a reception memory 416 and acontrol section 417.

Computation processes carried out by the computers 412 _(k) and thecomputers 415 _(k) (where k=1, 2, . . . and 6) are explained by makinguse of equations as follows.

To put it concretely, the computation section 412 carries out a firstcomputation process according to Eq. (7) given earlier and Eq. (8) shownbelow in order to generate a decoding intermediate result u_(j) as theresult of the first computation process and supplies to the decodingintermediate result storage memory 410. Computation section 415 carriesout a second computation process according to Eq. (5) given earlier inorder to generate a decoding intermediate result v as the result of thesecond computation process and supplies to the decoding intermediateresult storage memory 410.

[Eq. 8]v _(i) =v−u _(dv)  (8)

It is to be noted that notation u_(dv) used in Eq. (8) denotes anintermediate result received from an edge, which is included in the ithcolumn of the parity check matrix H as an edge serving as an object ofmessage computation, as a result of a check-node process. In this case,the intermediate result is the check-node process result itself. That isto say, notation u_(dv) denotes a decoding intermediate result for anedge serving as an object of message computation.

That is to say, the decoding intermediate result v obtained as a resultof the second computation process according to Eq. (5) given before isthe sum of the received value u_(oi) and decoding intermediate resultsu_(j) generated from all edges corresponding to matrix elements each setat 1 at intersections of rows and the ith column in the parity checkmatrix H as decoding intermediate results of check-node processes. Thus,the value v_(i) used in Eq. (7) is a difference obtained as a result ofsubtracting the decoding intermediate result u_(dv) received from anedge serving as an object of message computation as the decodingintermediate result of a check-node process from the decodingintermediate result v obtained as a result of the second computationprocess according to Eq. (5). The decoding intermediate result u_(dv) isone of the decoding intermediate results u_(j) generated from all edgescorresponding to matrix elements each set at 1 at intersections of rowsand the ith column in the parity check matrix H as decoding Intermediateresults of check-node processes. That is to say, the computation processexpressed by Eq. (1) as a process to compute the value v_(i) used in thecomputation process according to Eq. (7) is a computation processcarried out as a combination of the computation process according to Eq.(5) and Eq. (8).

Thus, in the decoding apparatus 400, the computation section 412 carriesout the first computation process according to Eqs. (7) and (8)alternately with the second computation process carried out by thecomputation section 415 in accordance with Eq. (5). Then, thecomputation section 415 outputs the result of the last secondcomputation process as a decoding result. In this way, the decodingapparatus 400 is capable of carrying out a decoding process repeatedlyto decode LDPC codes.

It is to be noted that the decoding intermediate result u_(j) obtainedas a result of the first computation process according to Eqs. (7) and(8) is equal to the result u_(j) of the check-node process according toEq. (7).

In addition, since the value v obtained as a result of the secondcomputation process according to Eq. (5) is a result of adding theresult u_(j) received from an edge serving as an object of messagecomputation as the result of a check-node process to the result v_(i) ofthe variable-node process according to Eq. (1), only one value v isfound for 1 column of the parity check matrix H (or for one variablenode).

In the decoding apparatus 400, the computation section 412 makes use ofthe decoding intermediate result v produced in the second computationprocess carried out by the computation section 415 as a resultcorresponding to columns of the parity check matrix H in execution ofthe first computation process. The computation section 412 generates adecoding intermediate result u_(j) as the result of the firstcomputation process and supplies to the decoding intermediate resultstorage memory 413. The decoding intermediate result u_(j) is generatedfrom an edge corresponding to a matrix element set at 1 at anintersection of a row and the ith column in the parity check matrix H asa decoding intermediate result of a check-node process of a check nodeoutputting a message through the edge. Thus, the storage capacity of thedecoding intermediate result storage memory 413 is equal to the productobtained as a result of an operation to multiply the number of onematrix elements in the parity check matrix H (that is, the number of alledges) by the number of quantization bits as is the case with thestorage capacity of a memory used for storing results of check-nodeprocesses.

On the other hand, the computation section 415 makes use of the decodingintermediate results u_(j) generated from all edges corresponding tomatrix elements each set at “1” at intersections of rows and the ithcolumn in the parity check matrix H as decoding intermediate results ofsecond computation processes carried out by the computation section 412and makes use of received data u_(oi) in order to carry out the secondcomputation process and stores a decoding intermediate result vcorresponding to the ith column in the decoding intermediate resultstorage memory 410 as a result of the second computation process. Thus,the storage capacity of the decoding intermediate result storage memory410 is equal to the product obtained as a result of an operation tomultiply the number of columns smaller than the number of matrixelements each set at 1 in the parity check matrix H, that is, the codelength of the LDPC codes by the number of quantization bits of thedecoding intermediate result v.

As a result, the storage capacity of the decoding intermediate resultstorage memory 410 can be reduced to a value smaller than the storagecapacity of a memory used for storing the result of a variable-nodeprocess. Thus, the circuit scale of the decoding apparatus 400 can bedecreased.

Next, operations carried out by the sections employed in the decodingapparatus 400 shown in FIG. 17 are explained in detail as follows.

The decoding intermediate result storage memory 410 is used for storingsix decoding intermediate results D415 generated by the computationsection 415 as a result of the second computation process carried out bythe computation section 415. The six decoding intermediate results D415generated by the computation section 415 are sequentially stored(memory) in the decoding intermediate result storage memory 410 atstorage locations starting with a first address.

To put it in detail, at the first address in the decoding intermediateresult storage memory 410, the first to sixth decoding intermediateresults v are stored as a part of decoding intermediate resultscorresponding to the columns of the parity check matrix H. Then, by thesame token, at a second address, the seventh to twelfth decodingintermediate results v are stored. Subsequently, in the same way, at athird address, the thirteenth to eighteenth decoding intermediateresults v are stored. Thereafter, the same operation to store sixdecoding intermediate results v at an address of a sequence of addressesstarting with a fourth address is carried out repeatedly in a similarmanner till the 103rd to 108th decoding intermediate results v arestored in an eighteenth address. As a result, 108 decoding intermediateresults v are stored in the decoding intermediate result storage memory410. Thus, the number of words in the decoding intermediate resultstorage memory 410 is a quotient of 18 obtained as a result of dividingthe integer 108 which is the number of columns (the code length of LDPCcodes) composing the parity check matrix H shown in FIG. 16 by theinteger 6 which is the number of decoding intermediate results at thesame time in one operation described above.

In addition, the decoding intermediate result storage memory 410 selectssix decoding intermediate results v corresponding to matrix elementseach set at “1” on a row included in the parity check matrix H as a rowcorresponding to a decoding intermediate result u_(j) to be found by thecomputation section 412 at a succeeding stage from the decodingintermediate results D415 already stored in the decoding intermediateresult storage memory 410 and outputs the six selected decodingintermediate results v to the cyclic shift circuit 411 at the same timeas a decoding intermediate result D410.

It is to be noted that the decoding intermediate result storage memory410 typically employs single-port RAMs allowing operations to store andread out six decoding intermediate results in any of the RAMs at thesame time. In addition, the decoding intermediate result storage memory410 is also used for storing a decoding intermediate result D414produced by the second computation process carried out by thecomputation section 415 as a result corresponding to a column. Thus, therequired storage capacity of the decoding intermediate result storagememory 410, that is, the maximum amount of data that can be stored inthe decoding intermediate result storage memory 410, is equal to aproduct obtained as a result of an operation to multiply thequantization-bit count of the decoding intermediate result D414 by thenumber of columns (the code length of LDPC codes) in the parity checkmatrix H.

The cyclic shift circuit 411 receives six decoding intermediate resultsD410 from the decoding intermediate result storage memory 410 and acontrol signal D619 from the control section 417. The control signalD619 is information on the number of cyclic shift operations to becarried out on components matrixes such as unit matrixes composing theparity check matrix H. To put it concretely, the information is matrixdata representing the number of matrix elements each set at 1 in theparity check matrix H as a matrix element corresponding to one of thedecoding intermediate results D410. On the basis of the control signalD619, the cyclic shift circuit 411 carries out cyclic shift operationsto rearrange the six decoding intermediate results D410 and outputs theresult of the arrangement to the computation section 412 as decodingintermediate results D411.

As described above, the computation section 412 employs the sixcomputers 412 ₁ to 412 ₆. The computation section 412 receives the sixdecoding intermediate results D411 (v) from the cyclic shift circuit 411as a result of the second computation process carried out by thecomputation section 415. In addition, the computation section 412 alsoreceives six decoding intermediate results D413 (u_(j)) from thedecoding intermediate result storage memory 413 as a result of the firstcomputation process previously carried out by the six computers 412 ₁ to412 ₆. The six decoding intermediate results D411 and the six decodingintermediate results D413 are supplied to the six computers 412 ₁ to 412₆ respectively. On top of that, the computation section 412 alsoreceives the control signal D419 from the control section 417. In thecomputation section 412, the control signal D419 is supplied to all thesix computers 412 ₁ to 412 ₆. It is to be noted that the control signalD419 is a signal common to the six computers 412 ₁ to 412 ₆.

The six computers 412 ₁ to 412 ₆ each carry out the first computationprocess according to Eqs. (7) and (8) by making use of one of the sixdecoding intermediate results D411 (v) and one of the six decodingintermediate results D413 in order to find six decoding intermediateresults D412 (v_(i)) corresponding to six matrix elements each set at 1in the parity check matrix H. Then, the computation section 412 outputsthe six decoding intermediate results D412 obtained as a result of theprocesses carried out by the six computers 412 ₁ to 412 ₆ respectivelyto the decoding intermediate result storage memory 413.

The decoding intermediate result storage memory 413 typically employstwo single-port RAMs allowing operations to write and read out sixdecoding intermediate results to and from any of the RAMs at the sametime. The decoding intermediate result storage memory 413 receives thesix decoding intermediate results D412 from the computation section 412and a control signal D420 from the control section 417 as a signal forcontrolling an operation to write and read out the six decodingintermediate results D413 to and from the decoding intermediate resultstorage memory 413.

The decoding intermediate result storage memory 413 allows the sixdecoding intermediate results D412 received from the computation section412 to be collectively stored therein and six decoding intermediateresults D412 already stored in the decoding intermediate result storagememory 413 to be read out at the same time on the basis of the controlsignal D420. The decoding intermediate result storage memory 413supplies the six decoding intermediate results D412 already storedtherein to the computation section 412 and the cyclic shift circuit 414as the six decoding intermediate results D413. That is to say, thedecoding intermediate result storage memory 413 allows an operation toread out six decoding intermediate results D413 to be supplied to thecomputation section 412 and the cyclic shift circuit 414 and anoperation to store the six decoding intermediate results D412 receivedfrom the computation section 412 at the same time.

It is to be noted that the decoding intermediate results D412 resultingfrom the first computation process carried out by the computationsection 412 are stored in the decoding intermediate result storagememory 413 as messages each generated from an edge corresponding to amatrix element set at 1 at an intersection of a row and the ith columnin the parity check matrix H. Thus, the required storage capacity of thedecoding intermediate result storage memory 413, that is, the amount ofdata that can be stored in the decoding intermediate result storagememory 413, is equal to a product obtained as a result of an operationto multiply the quantization-bit count of the decoding intermediateresult D412 by the number of matrix elements each set at 1 in the paritycheck matrix H.

The cyclic shift circuit 414 receives six decoding intermediate resultsD413 (decoding intermediate results u_(j)) from the decodingintermediate result storage memory 413 and a control signal D421 fromthe control section 417. The control signal D421 is information on thenumber of cyclic shift operations to be carried out on componentsmatrixes such as unit matrixes composing the parity check matrix H. Toput it concretely, the information is matrix data representing thenumber of matrix elements each set at 1 in the parity check matrix H asa matrix element corresponding to one of the decoding intermediateresults D413. On the basis of the control signal D421, the cyclic shiftcircuit 414 carries out cyclic shift operations to rearrange the sixdecoding intermediate results D413 and outputs the result of thearrangement to the computation section 415 as decoding intermediateresults D414.

As described earlier, the computation section 415 employs the sixcomputers 415 ₁ to 415 ₆. The computation section 415 receives the sixdecoding intermediate results D414 from the cyclic shift circuit 414.The six decoding intermediate results D414 are supplied to the 6computers 415 ₁ to 415 ₆ respectively. In addition, the computationsection 415 also receives six pieces of received data D417 (or the LDPCcodes) from the reception memory 417. The received data D417 aresupplied to the six computers 415 ₁ to 415 ₆ respectively. On top ofthat, the computation section 417 also receives a control signal D422from the control section 417. The control signal D422 is supplied to thecomputers 415 ₁ to 415 ₆. It is to be noted that the control signal D422is a signal common to the computers 417 ₁ to 417 ₆.

The computers 415 ₁ to 415 ₆ each carry out the second computationprocess according to Eq. (5) by making use of the decoding intermediateresults D414 and the decoding intermediate results D417 in order to finddecoding intermediate results D415. Then, the computation section 415supplies the six decoding intermediate results D415 (v) obtained as aresult of the second computation processes carried out by the computers415 ₁ to 415 ₆ respectively to the decoding intermediate result storagememory 410. If the process presently carried out by the computationsection 415 is the last second computation process, the six decodingintermediate results D415 obtained as a result of the processes areoutput as the final decoding result.

The reception memory 416 is a memory used for storing received dataD416, which is data (received data) of a received LLR (Log LikelihoodRatio) serving as the value of a 0 likelihood computed from an incomingvalue (or a sign bit) D416 received from a transmission line as the 0likelihood of the sign bit.

To put it in detail, at a first address in the reception memory 416,received data D416 corresponding to the first to sixth columns of theparity check matrix H are stored as a part of received data D416corresponding to the columns of the parity check matrix H. Then, by thesame token, at a second address, received data D416 corresponding to theseventh to twelfth columns of the parity check matrix H are stored.Subsequently, in the same way, at a third address, received data D416corresponding to the thirteenth to eighteenth columns of the paritycheck matrix H are stored. Thereafter, the same operation to store sixpieces of received data D416 at an address in a sequence of addressesstarting with a fourth address is carried out repeatedly in a similarmanner till received data D416 corresponding to the 19th to 108thcolumns of the parity check matrix H are stored in an eighteenthaddress.

Then, pieces of received data D416 already stored in the receptionmemory 616 are read out in 6-piece units sequentially one unit afteranother in an order required by a variable-node process and supplied tothe computation section 415 as received data D417.

It is to be noted that the reception memory 416 typically employssingle-port RAMs allowing operations to write and read out six pieces ofreceived data to and from any of the RAMs at the same time. Thus, therequired storage capacity of the reception memory 416, that is, themaximum amount of data that can be stored in the reception memory 416,is equal to a product obtained as a result of an operation to multiplythe quantization-bit count of the received data D416 by the code lengthof the LDPC codes. In addition, the number of words in the receptionmemory 416 is a quotient of 18 obtained as a result of dividing theinteger 108 by the integer 6. In this case, the integer 108 is thenumber of columns composing the parity check matrix H, that is the codelength of the LDPC codes whereas the integer 6 is the number of piecesof received data D417 read out at the same time in one operationdescribed above.

The control section 417 supplies the control signal D418 to the cyclicshift circuit 411 in order to control the cyclic shift circuit 411 andthe control signal D419 to the computation section 412 in order tocontrol the computation section 412. In addition, the control sectionsupplies the control signal D420 to the decoding intermediate resultstorage memory 413 in order to control the decoding intermediate resultstorage memory 413, the control signal D421 to the cyclic shift circuitin order to control the cyclic shift circuit 414 and the control signalD421 to the computation section 415 in order to control the computationsection 415.

Data is circulated for one decoding process in the decoding apparatus400 in the following order: the decoding intermediate result storagememory 410 to the cyclic shift circuit 411 to the computation section412 to the decoding intermediate result storage memory 413 to the cyclicshift circuit 414 and to the computation section 415. After the decodingapparatus 400 carries out the decoding process repeatedly apredetermined number of times, the decoding intermediate results D415obtained as a result of the second computation processes carried out bythe computation section 415 are output as the final decoding result.

FIG. 18 is a block diagram showing a typical configuration of acomputation section 412 ₁ employed in the computation section 412 shownin FIG. 17.

It is to be noted that, even though the computation section 412 ₁ isexplained by referring to FIG. 18, the explanation also applies to thecomputers 412 ₂ to 412 ₆.

In the configuration shown in FIG. 18 as the configuration of thecomputation section 412, each decoding intermediate result (u_(dv))obtained as a result of the first computation process carried outpreviously by the computation section 412 is quantized into dataincluding 6 bits including a sign bit whereas each decoding intermediateresult (v) obtained as a result of the second computation processcarried out by the computation section 415 is quantized into dataincluding 9 bits. In addition, the computer 412 ₁ shown in FIG. 18receives a clock signal ck to be provided to necessary blocks. Thus,each block employed in the computer 412 ₁ carries out an operationsynchronously with the clock signal ck.

On the basis of the control signal D419 received from the controlsection 417, the computer 412 ₁ shown in FIG. 18 carries out the firstcomputation process according to Eqs. (7) and (8) by making use of adecoding intermediate result D413 (u_(dv)) obtained as a result of thefirst computation process performed earlier by the computation section412 and one of decoding intermediate results D411 (v) suppliedsequentially one result after another by the cyclic shift circuit 411.The decoding intermediate results D413 (u_(dv)) are read out from thedecoding intermediate result storage memory 413 sequentially one resultafter another.

To be more specific, the computer 412 ₁ receives one of six 9-bitdecoding intermediate result D411 (v) supplied sequentially one resultafter another by the cyclic shift circuit 411 and a decodingintermediate result D413 (u_(dv)) selected from six 6-bit decodingintermediate results D413 (u_(j)) read out from the decodingintermediate result storage memory 413 sequentially one result afteranother. As described above, the 6-bit decoding intermediate result D413(u_(dv)) is obtained as a result of the first computation processperformed earlier by the computation section 412. In the computer 412 ₁,the decoding intermediate result D411 (v) including 9 bits and thedecoding intermediate result D413 (u_(dv)) including bits are suppliedto an adder 431. In addition, the computer 412 ₁ also receives thecontrol signal D419 from the control section 417. The control signalD419 is supplied to selectors 435 and 442.

The adder 431 subtracts the decoding intermediate result D413 (u_(j))including 6 bits from the decoding intermediate result D411 (v)including 9 bits to yield a difference D431 including 6 bits. That is tosay, the adder 431 carries out an operation according to Eq. (8) inorder to produce the difference D431 (v_(i)) as the result of theoperation.

The 1-bit sign bit D432 (sign (v_(i))) of the 6-bit difference D431generated by the adder 431 is supplied to an EXOR circuit 440 whereasthe 5 less significant bits D433 (|v_(i)|) of the difference D431including 6 bits are supplied to a LUT 432. The sign bit D432 (sign(v_(i))) representing the plus/minus sign of the 6-bit difference D431is the most significant bit of the 6-bit difference D431.

For the absolute value D433 (|v_(i)|) supplied to the LUT 432, the LUT432 reads out 5-bit data D434 (φ(|v_(i)|) used in the computationprocess according to Eq. (7)) from a table and supplies the data D434(φ(|v₁|)) to an adder 433 and a FIFO memory 438.

The adder 433 cumulatively adds the data D434 (or the value of thefunction φ(|v_(i)|)) to 9-bit data D435 stored in a register 434 inorder to compute a sum D434 including 9 bits and stores the sum D434back in the register 434. It is to be noted that this cumulativeaddition process is carried out repeatedly and, as the cumulativeaddition process is completed to find the final cumulative additionresult for the absolute values D433 (|v_(i)|) found from the decodingintermediate results D411 corresponding to all matrix elements set at 1on 1 row of the parity check matrix H, the contents of the register 434are reset.

After receiving decoding intermediate results D411 corresponding to arow of the parity check matrix H sequentially one result after anotherand sequentially adding the results D411 to the data D434 stored in theregister 434 in a cumulative manner, the control section 417 changes thecontrol signal D419 supplied thereby from 0 to 1. In the case of a rowweight of 9 for example, the control signal D419 stays at 0 during aperiod covering the first to eighth clock pulses. As the ninth clockpulse is generated, the control section 417 changes the control signalD419 to 1.

With the control signal D419 set at 1, a selector 435 selects the datastored in the register 434 and supplies the data to a register 436 to bestored in the register 436 as data D436. The data stored in the register434 with the control signal D419 set at 1 is 9-bit data D435 obtained asa result of cumulatively adding the function values φ(|v_(i)|) foundfrom decoding intermediate results D411 (or decoding intermediateresults v) corresponding to all matrix elements set at 1 on 1 row of theparity check matrix H. That is to say, the cumulative 9-bit data D435 isthe value of Σφ(|v_(i)|) for a summation range starting from i=1 andending at i=d_(c). The data D436 stored in the register 436 is suppliedto the selector 435 and an adder 437 as data D437 including 9 bits. Withthe control signal D419 reset at 0, on the other hand, the selector 435selects the 9-bit data D437 received from the register 436 and outputsthe selected data D437 to the register 436 as data to be stored in theregister 436 again. That is to say, the register 436 supplies the 9-bitdata D437 obtained as a result Σφ(|v_(i)|) of the cumulative additionscarried out previously to the selector 435 and the adder 437 till dataincluding 9 bits is obtained as a result Σφ(|v_(i)|) of cumulativelyadding the function values φ(|v_(i)|) found from the decodingintermediate results D411 (or the decoding intermediate results v)corresponding to all matrix elements set at 1 on 1 row of the paritycheck matrix H.

On the other hand, a FIFO memory 438 delays the computation result D434(φ(|v_(i)|)) received from the LUT 432 to a point of time at which theregister 436 supplies new data D437 (Σφ(|v_(i)|) for a summation rangestarting from i=1 and ending at i=d_(c)) to the adder 437. Then, theFIFO memory 438 supplies the delayed data D434 to an adder 437 as dataD438 including 5 bits. The adder 437 subtracts the data D438 supplied bythe FIFO memory 438 from the data D437 supplied by the register 436.That is to say, the adder 437 subtracts a decoding intermediate resultcorresponding to an edge serving as an object of message computation,that is, the function value φ(|v_(i)|) found from the decodingintermediate result D411 (or the decoding intermediate result v)corresponding to a predetermined matrix element set at 1 on 1 row of theparity check matrix H, from the result Σφ(|v_(i)|) of cumulativelyadding the function values φ(|v_(i)|) found from the decodingintermediate results D411 (or the decoding intermediate results v)corresponding to all matrix elements set at 1 on the row of the paritycheck matrix H, and outputs the difference to a LUT 439 as a differenceD439. The difference D439 is thus the value of Σφ(|v_(i)|) for asummation range starting from i=1 and ending at i=(d_(c)−1).

For the difference D439 representing the value of Σφ(|v_(i)|) for asummation range starting from i=1 and ending at i=(d_(c)−1), the LUT 439reads out a 5-bit computation result D440 (φ⁻¹(Σφ(|v_(i)|)) used in thecomputation process according to Eq. (7)).

Concurrently with the processing described above, an EXOR circuit 440computes the exclusive logical sum of 1-bit data D442 stored in aregister 441 and the sign bit D432. That is to say, the EXOR circuit 440computes the product of two sign bits. The multiplication result D441including 1 bit is stored back in the register 441. It is to be notedthat, when the sign bits D432 extracted from the decoding intermediateresults D411 corresponding to all matrix elements set at 1 on 1 row ofthe parity check matrix H have been subjected to the multiplicationprocess carried out by the EXOR circuit 440, the contents of theregister 441 are reset.

When the multiplication result D441 (or the value of Π sign (v_(i)) fora multiplication range starting from i=1 and ending at i=d_(c)) obtainedfrom the multiplication processes carried out on the sign bits D432extracted from the decoding intermediate results D411 corresponding toall matrix elements set at 1 on 1 row of the parity check matrix H isstored in the register 441, the control section 417 changes the controlsignal D419 supplied thereby from 0 to 1.

With the control signal D419 set at 1, a selector 442 selects themultiplication result D442 (Π sign (v_(i)) for a multiplication rangestarting from i=1 and ending at i=d_(c)) stored in the register 441 andsupplies the multiplication result D442 to a register 443 as 1-bit dataD443 to be stored in the register 443. As described above, themultiplication result D442 is a 1-bit data obtained as a result of themultiplication processes carried out by the EXOR circuit 445 on the signbits D432 extracted from the decoding intermediate results D411corresponding to all matrix elements set at 1 on 1 row of the paritycheck matrix H. The data D443 stored in the register 443 is supplied tothe selector 442 and an EXOR circuit 445 as data D444 including 1 bit.With the control signal D419 reset at 0, on the other hand, the selector442 selects the data D444 received from the register 443 and outputs tothe register 443 as data to be stored in the register 443 again. That isto say, the register 443 supplies the data already stored therein to theselector 442 and the EXOR circuit 445 till data is obtained as a resultof the multiplication processes on the sign bits D432 extracted from thedecoding intermediate results D411 (or the decoding intermediate resultsv) corresponding to all matrix elements set at 1 on 1 row of the paritycheck matrix H.

On the other hand, the FIFO memory 444 delays the sign bit D432 to apoint of time at which the register 443 supplies new data D444 (or thevalue of Π sign (v_(i)) for a multiplication range starting from i=1 andending at i=d_(c)) to the EXOR circuit 445. Then, the FIFO memory 444supplies the delayed sign bit D432 to the EXOR circuit 445 as data D445including 1 bit. The EXOR circuit 445 computes an exclusive logical sumof the data D444 received from the register 443 and the 1-bit data D445received from the FIFO memory 444 in order to divide the data D444 bythe data D445, and outputs the division result consisting of 1 bit asdata D446. That is to say, the EXOR circuit 445 divides a product ofdecoding intermediate results D432 (sign (v_(i))) extracted fromdecoding intermediate results D411 corresponding to all matrix elementsset at 1 on 1 row of the parity check matrix H by the sign bit D432(sign (v_(i))) extracted from a decoding intermediate result D411corresponding to a predetermined matrix element set at 1 on the row ofthe parity check matrix H, and outputs the division result (or the valueof Π sign (v_(i)) for a multiplication range starting from i=1 andending at i=(d_(c)−1)) as the division result D446.

The computer 412 ₁ concatenates the 5-bit processing result D440generated by the LUT 439 with the 1-bit division result D446 produced bythe EXOR circuit 445 by taking the processing result D440 including 5bits as 5 less significant bits and the division result D446 including 1bit as the most significant bit in order to output a decodingintermediate result D412 (or a decoding intermediate result u_(j))including a total of 6 bits.

As described above, the computer 142 ₁ carries out the computationprocessing according to Eqs. (7) and (8) in order to find a decodingintermediate result u_(j).

It is to be noted that, since the maximum value of the row weight forthe parity check matrix H shown in FIG. 16 is 9, that is, since themaximum number of decoding intermediate results D411 (v) and decodingintermediate results D413 (u_(dv)) supplied to the computer 412 ₁ areeach 9, the computer 412 ₁ is provided with the FIFO memory 438 fordelaying the nine decoding intermediate results D434 (or the values ofthe function φ(|v_(i)|)) and the FIFO memory 444 for delaying the ninesign bits D432. In a process to handle row messages fewer than the rowweight of 9, the magnitude of the delay provided by the FIFO memory 438and the FIFO memory 444 can be reduced to a value corresponding to therow weight.

FIG. 19 is a block diagram showing a typical configuration of a computer415 ₁ employed in the computation section 415 shown in FIG. 17.

It is to be noted that, even though only the computer 415 ₁ is explainedby referring to FIG. 19, the explanation also applies to the computers415 ₂ to 415 ₆.

In the configuration shown in FIG. 19 as the configuration of thecomputer 415 ₁, each decoding intermediate result (u_(j)) obtained as aresult of the first computation process carried out by the computationsection 412 is quantized into a total of 6 bits including a sign bit. Inaddition, the computer 415 ₁ shown in FIG. 19 receives a clock signal ckproviding the necessary clock signal ck to the computer 415 ₁. Thus,each block employed in the computer 415 ₁ carries out an operationsynchronously with the clock signal ck.

On the basis of a control signal D422 received from the control section417, the computer 415 ₁ shown in FIG. 19 carries out the secondcomputation process according to Eq. (5) by making use of pieces ofreceived data D417 (or received values u_(oi)) sequentially read outfrom the reception memory 416 one piece after another and decodingintermediate results D414 (u_(j)) sequentially read out from the cyclicshift circuit 414 one result after another.

That is to say, the computer 415 ₁ reads out 6-bit decoding intermediateresults D414 (or decoding intermediate results u_(j)) corresponding tomatrix elements set at 1 on rows of the parity check matrix H from thecyclic shift circuit 414 sequentially one result after another from thecyclic shift circuit 414, supplying the decoding intermediate resultsD414 to an adder 471. In addition, the computer 415 ₁ reads out piecesof 6-bit received D417 from the reception memory 416 sequentially onepiece after another, supplying the pieces of 6-bit received D417 to anadder 475. On top of that, the computer 415 ₁ receives a control signalD422 from the control section 417 and supplies the control signal D422to a selector 473.

The adder 471 adds the decoding intermediate result D414 (or thedecoding intermediate result u_(j)) to 9-bit data D471 stored in aregister 472 in order to produce a cumulative decoding intermediate D414consisting of 9 bits and stores the cumulative decoding intermediateresult D414 consisting of 9 bits also in the register 472. It is to benoted that, after the decoding intermediate results D414 correspondingto all matrix elements set at 1 on 1 column of the parity check matrix Hare cumulatively added and stored in the register 472, the contents ofthe register 472 are reset.

After the computer 415 ₁ reads out decoding intermediate results D414corresponding to all matrix elements set at 1 on 1 column of the paritycheck matrix H sequentially one result after another and stores thecumulative decoding intermediate result D414 to the register 472, thecontrol section 417 changes the control signal D422 supplied therebyfrom “0” to “1”. In the case of a column weight of “5” for example, thecontrol signal D422 stays at “0” during a period covering the first tofourth clock pulses. As the fifth clock pulse is generated, the controlsection 417 changes the control signal D422 from “0” to “1”.

With the control signal D422 set at “1”, a selector 473 selects thevalue stored in the register 472, that is the 9-bit cumulative sum D471(value of Σu_(j) for a summation range starting from j=1 and ending atj=d_(v)) stored in the register 472 and supplies the cumulative sum D471consisting of 9 bits to a register 474 to be stored in the register 474.The cumulative sum D471 stored in the register 472 is a 9-bit valueobtained as a result of cumulatively adding the decoding intermediateresults D414 (or decoding intermediate results u_(j)) received from allthe edges along 1 column of the parity check matrix H. The data D471stored in the register 474 is supplied to the selector 471 and an adder475 as data D472 consisting of 9 bits. With the control signal D422reset at “0”, on the other hand, the selector 473 selects the data D472received from the register 474 and outputs to the register 474 as datato be stored in the register 474 again. That is to say, the register 474supplies the 9-bit data D472 obtained as a result of the cumulativeadditions carried out previously to the selector 473 and the adder 475till the decoding intermediate results D414 (or decoding intermediateresults u_(j)) received from all the edges along 1 column of the paritycheck matrix H are added to each other in order to give a cumulativesum.

The adder 475 adds the data D472 consisting of 9 bits to the 6-bit dataD417 received from the reception memory 416 and outputs a decodingintermediate result D415 (or a decoding intermediate result v) obtainedas the result of the addition operation.

As described above, the computer 415 ₁ carries out a process accordingto Eq. (5) in order to produce the decoding intermediate result v.

It is to be noted that, since the maximum value of the column weight forthe parity check matrix H shown in FIG. 9 is 5, that is, since themaximum number of decoding intermediate results u_(j) supplied to thecomputer 415 ₁ is 5, the computer 415 ₁ adds up to five decodingintermediate results u_(j) each consisting of 6 bits in order to give acumulative sum. Thus, the output of the computer 415 ₁ consists of 9bits.

FIG. 20 is a block diagram showing a typical configuration of thedecoding intermediate result storage memory 413 shown in FIG. 17.

The decoding intermediate result storage memory 413 employs switches 501and 504 as well as two decoding intermediate result storage RAMs 502 and503, which are each a single-port RAM.

Before every component employed in the decoding intermediate resultstorage memory 413 is described in detail, first of all, a method forstoring data in the decoding intermediate result storage RAMs 502 and503 is described.

The decoding intermediate result storage RAMs 502 and 503 are each usedfor storing decoding intermediate results D412 supplied to the decodingintermediate result storage RAMs 502 and 503 by way of the switch 501 asa result of the first computation process carried out by the computationsection 412.

To put it concretely, at first to ninth addresses in the decodingintermediate result storage RAM 502, decoding intermediate results D412(D501) corresponding to matrix elements set at 1 on the first to sixthrows of the parity check matrix H shown in FIG. 16 are stored in a formof packing (by ignoring matrix elements reset to 0) decodingintermediate results D412 corresponding to matrix elements set at 1 onthe rows in the horizontal direction (or the column arrangementdirection).

Let notation (j, i) denote an intersection of the jth row and the ithcolumn in the parity check matrix H shown in FIG. 16. In this case,decoding intermediate results D412 corresponding to matrix elements setat 1 in a 6×6 unit matrix included in the parity check matrix H shown inFIG. 16 as a component matrix spread throughout a matrix area rangingover intersections (1, 1) to (6, 6) are stored at the first address inthe decoding intermediate result storage RAM 502. By the same token,decoding intermediate results D412 corresponding to matrix elements setat 1 in a 6×6 shift matrix included in the parity check matrix H shownin FIG. 16 as a component matrix spread throughout a matrix area rangingover intersections (1, 25) to (6, 30) are stored at the second address.The shift matrix in this case is a shift matrix obtained by carrying outa cyclic shift operation on a 6×6 unit matrix by 5 matrix elements inthe direction to the right. In the same way, decoding intermediateresults D412 corresponding to matrix elements set at 1 in 6 componentmatrixes included in the parity check matrix H shown in FIG. 16 arestored at the third to eighth addresses. Likewise, decoding intermediateresults D412 corresponding to matrix elements set at 1 in a 6×6 shiftmatrix included in the parity check matrix H shown in FIG. 16 as acomponent matrix spread throughout a matrix area ranging overintersections (1, 102) to (6, 108) are stored at the ninth address. Theshift matrix in this case is a shift matrix obtained by carrying out acyclic shift operation on a 6×6 semi unit matrix by 1 matrix element inthe direction to the right. The 6×6 semi unit matrix in this case is asemi unit matrix obtained by resetting the matrix element set at 1 onthe first row of a 6×6 unit matrix to 0. In this case, the first row ofthe 6×6 shift matrix spread throughout a matrix area ranging overintersections (1, 102) to (6, 108) does not include a matrix element setat 1. Thus, no decoding intermediate results D412 are stored at theninth address.

By the same token, at tenth to eighteenth addresses in the decodingintermediate result storage RAM 502, decoding intermediate results D412(D501) corresponding to matrix elements set at 1 on the thirteenth toeighteenth rows of the parity check matrix H shown in FIG. 16 arestored. To put it in detail, decoding intermediate results D412corresponding to matrix elements set at 1 in a 6×6 shift matrix includedin the parity check matrix H shown in FIG. 16 as a component matrixspread throughout a matrix area ranging over intersections (13, 7) to(18, 12) are stored at the tenth address. The shift matrix in this caseis a shift matrix obtained by carrying out a cyclic shift operation on a6×6 unit matrix by 5 matrix elements in the direction to the right. Bythe same token, decoding intermediate results D412 corresponding tomatrix elements set at 1 in a shift matrix serving as a component of asum matrix included in the parity check matrix H shown in FIG. 16 as acomponent matrix spread throughout a matrix area ranging overintersections (13, 13) to (18, 18) are stored at the eleventh address.The sum matrix in this case is the sum of a 6×6 unit matrix and theshift matrix, which is obtained by carrying out a cyclic shift operationon a 6×6 unit matrix by 1 matrix element in the direction to the right.Likewise, decoding intermediate results D412 corresponding to matrixelements set at 1 in the 6×6 the unit matrix serving as a component ofthe sum matrix included in the parity check matrix H shown in FIG. 16 asa component matrix spread throughout a matrix area ranging overintersections (13, 13) to (18, 18) are stored at the twelfth address.Thereafter, in the same way, decoding intermediate results D412corresponding to matrix elements set at 1 in component matrixes includedin the parity check matrix H shown in FIG. 16 are stored at thethirteenth to eighteenth addresses.

That is to say, in the case of a component matrix having a weight 2 ormore, the component matrix is expressed in the form of a sum matrixobtained by computing the sum of a P×P unit matrix having a weight of 1,a semi unit matrix having a weight of 1 and a shift matrix having aweight of 1. As described earlier, a semi unit matrix is a matrixobtained by setting one or more of the elements set at 1 in a unitmatrix to 0 whereas a shift matrix is a matrix obtained by carrying outa cyclic shift operation on a unit matrix or a semi unit matrix. Withthe component matrix expressed in the form of a sum matrix as describedabove, decoding intermediate results (decoding intermediate resultsobtained in the course of a process to decode messages corresponding toedges corresponding to matrix elements set at 1 in the unit matrix, thesemi unit matrix and the shift matrix) corresponding to matrix elementsset at 1 in the unit matrix having a weight of 1, the semi unit matrixhaving a weight of 1 and the shift matrix having a weight of 1 arestored at the same address.

By the same token, decoding intermediate results D412 corresponding tomatrix elements set at 1 on the twenty-fifth to thirtieth rows of theparity check matrix H shown in FIG. 16 are stored at nineteenth totwenty-seventh addresses in the decoding intermediate result storage RAM502. That is to say, the number of words of the decoding intermediateresult storage RAM 502 is 27.

On the other hand, at first to ninth addresses in the decodingintermediate result storage RAM 503, decoding intermediate results D412(D502) corresponding to matrix elements set at 1 on the seventh totwelfth rows of the parity check matrix H shown in FIG. 16 are stored ina form of packing (ignoring matrix elements reset to 0) decodingintermediate results D412 corresponding to matrix elements set at 1 onthe rows in the horizontal direction (or the column arrangementdirection).

To be more specific, a first shift matrix of a sum matrix (the sum ofthe first shift matrix obtained by carrying out a cyclic shift operationon a 6×6 unit matrix by 2 matrix elements in the direction to the rightand a second shift matrix obtained by carrying out a cyclic shiftoperation on a 6×6 unit matrix by 4 matrix elements in the direction tothe right) included in the parity check matrix H as a component matrixspread throughout a matrix area ranging over intersections (7, 1) to(12, 6) are stored at the first address in the decoding intermediateresult storage RAM 503. By the same token, a second shift matrix of thesum matrix included in the parity check matrix H as a component matrixspread throughout a matrix area ranging over intersections (7, 1) to(12, 6) are stored in the second address. Thereafter, in the same way,component matrixes included in the parity check matrix H are stored atthe third to ninth addresses.

By the same token, at tenth to eighteenth addresses in the decodingintermediate result storage RAM 503, decoding intermediate results D412(D502) corresponding to matrix elements set at 1 on the nineteenth totwenty-fourth rows of the parity check matrix H shown in FIG. 16 arestored. In the same way, at nineteenth to twenty-seventh addresses inthe decoding intermediate result storage RAM 503, decoding intermediateresults D412 (D502) corresponding to matrix elements set at 1 on thethirty-first to thirty-sixth rows of the parity check matrix H shown inFIG. 16 are stored. That is to say, the number of words of the decodingintermediate result storage RAM 503 is 27.

As described above, the number of words in the decoding intermediateresult storage RAM 502 and the number of words in the decodingintermediate result storage RAM 503 are each 27. This number is obtainedas follows. The row weight of the parity check matrix H is 9. This rowweight of 9 is multiplied by the row count of 36 to give a product,which is equal to the number of matrix elements set at 1 in the paritycheck matrix H. The product is then divided by the number of decodingintermediate results to give a quotient. The number of decodingintermediate results is the number of decoding intermediate results thatcan be read out from the decoding intermediate result storage RAM 502 orthe decoding intermediate result storage RAM 503 at the same time. Inthis case, the number of decoding intermediate results D501, which canbe read out from the decoding intermediate result storage RAM 502 or thedecoding intermediate result storage RAM 503 respectively at the sametime, is 6. Finally, the quotient is further divided by the number ofRAMs employed in decoding intermediate result storage memory 413 toresult in the number 27. In this case, the number of RAMs employed indecoding intermediate result storage memory 413 is 2.

The following description explains details of operations carried out bysections employed in the decoding intermediate result storage memory 413shown in FIG. 20.

In the decoding intermediate result storage memory 413, when the firstcomputation process carried out by the computation section 412, thedecoding intermediate results D412 (u_(j)) of the first computationprocess carried out by the computation section 412 are provided and theintermediate results D412 is written to predetermined address in eitherof the decoding intermediate result storage RAM 502 and the decodingintermediate result storage RAM 503. At the same time, decodingintermediate results D412 (u_(j)) of the first computation processcarried out by the computation section 412 are read out from the otherone of the decoding intermediate result storage RAM 502 and the decodingintermediate result storage RAM 503 and outputted to the computationsection 412. When the computation section 415 carries out the secondcomputation process, on the other hand, the decoding intermediate resultstorage memory 413 is not used for writing the decoding intermediateresults of the second computation process in the decoding intermediateresult storage RAM 502 or the decoding intermediate result storage RAM503. Instead, the decoding intermediate result storage memory 413 readsout decoding intermediate results from a predetermined address in eitherthe decoding intermediate result storage RAM 502 or the decodingintermediate result storage RAM 503 and supplies the decodingintermediate results to the cyclic shift circuit 414.

The switch 501 receives six decoding intermediate results D412 from thecomputation section 412 and a control signal D420 ₁ as a signal forselecting either the decoding intermediate result storage RAM 502 or thedecoding intermediate result storage RAM 503 as a memory to be used forstoring the decoding intermediate results D412. On the basis of thecontrol signal D420 ₁, the switch 501 selects either the decodingintermediate result storage RAM 502 or the decoding intermediate resultstorage RAM 503 and supplies the six decoding intermediate results D412to the selected one of the decoding intermediate result storage RAM 502and the decoding intermediate result storage RAM 503.

Thus, the decoding intermediate result storage RAM 502 may receive thesix decoding intermediate results D412 from the switch 501 as decodingintermediate results D501. In this case, the decoding intermediateresult storage RAM 502 also receives a control signal D420 ₂representing an address from the control section 417. In addition, sixdecoding intermediate results D501 already stored at the addressrepresented by the control signal D420 ₂ as a result of the firstcomputation process carried out previously by the computation section412 are read out from the address and supplied to a switch 504 asdecoding intermediate results D503. Furthermore, the six decodingintermediate results D412 received from the switch 501 as decodingintermediate results D501 are stored (written) at the addressrepresented by the control signal D420 ₂.

As an alternative, the decoding intermediate result storage RAM 503receives the six decoding intermediate results D412 from the switch 501as decoding intermediate results D502. In this case, the decodingintermediate result storage RAM 503 also receives a control signal D420₃ representing an address from the control section 417. In addition, sixdecoding intermediate results D502 already stored at the address as aresult of the first computation process carried out previously by thecomputation section 412 are read out from the address and supplied tothe switch 504 as decoding intermediate results D504. Furthermore, thesix decoding intermediate results D502 received from the switch 501 arestored (written) at the address represented by the control signal D420₃.

The switch 504 receives the decoding intermediate results D503 from thedecoding intermediate result storage RAM 502 or the decodingintermediate results D504 from the decoding intermediate result storageRAM 503. In addition, the switch 504 also receives a control signal D420₄ generated by the control section 417 as a signal for selecting eitherthe decoding intermediate result storage RAM 502 or the decodingintermediate result storage RAM 503. On the basis of the control signalD420 ₄, the switch 504 selects either the decoding intermediate resultstorage RAM 502 or the decoding intermediate result storage RAM 503 as asource for the decoding intermediate results D413 to be output by theswitch 504. The switch 504 then passes on the six decoding intermediateresults received from the selected one of the decoding intermediateresult storage RAM 502 and the decoding intermediate result storage RAM503 to the computation section 412 and the cyclic shift circuit 414 asthe six decoding intermediate results D413.

FIG. 21 shows timing charts used for explaining read and writeoperations carried out on the decoding intermediate result storage RAM502 and the decoding intermediate result storage RAM 503, which areemployed in the decoding intermediate result storage memory 413.

It is to be noted that, in the timing charts shown in FIG. 21, thehorizontal axis represents the lapse of time (t). Notation Ri denotes anoperation to read out data corresponding to a matrix element indicatedby the suffix i enclosed in a circle in a component matrix shown in FIG.22 to indicate that the matrix element is a matrix element set at 1. Bythe same token, notation Wi denotes an operation to write (store) datacorresponding to a matrix element indicated by the suffix i enclosed ina circle in a component matrix shown in FIG. 22 to indicate that thematrix element is a matrix element set at 1.

When the computation section 412 carries out the first computationprocess, six decoding intermediate results D501 per clock are read outfor nine consecutive (9 clocks) in respectively (R0 to R8 shown in thefigure) on the basis of the control signal D420 ₂ from the same addressin the decoding intermediate result storage RAM 502 employed in thedecoding intermediate result storage memory 413. The decodingintermediate results D501 corresponding to matrix elements set at 1 onthe first to sixth rows of the parity check matrix H are a part ofdecoding intermediate results D501 already stored in the decodingintermediate result storage RAM 502 as a result of the first computationprocess carried out previously by the computation section 412. Thedecoding intermediate results D501 read out from the decodingintermediate result storage RAM 502 are supplied to the computationsection 412 by way of the switch 504. That is, since the row weight ofthe parity check matrix H shown in FIG. 16 is 9, the number of decodingintermediate results D501 corresponding to matrix elements set at 1 oneach of the first to sixth rows of the parity check matrix H is 9. Sincesix decoding intermediate results D501 are corresponding to matrixelements set at 1 on the first to sixth rows of the parity check matrixH are read out from the decoding intermediate result storage RAM 502 innine consecutive.

Then, six decoding intermediate results D502 per clock are read out for9 clocks in respectively read operations R9 to R17 shown in the figureon the basis of the control signal D420 ₃ from the same address in thedecoding intermediate result storage RAM 503. The decoding intermediateresults D502 corresponding to matrix elements set at 1 on the seventh totwelfth rows of the parity check matrix H are a part of decodingintermediate results D501 already stored in the decoding intermediateresult storage RAM 503 as a result of the first computation processcarried out previously by the computation section 412. The decodingintermediate results D502 read out from the decoding intermediate resultstorage RAM 503 are supplied to the computation section 412 by way ofthe switch 504.

The computers 412 ₁ to 412 ₆ and 415 ₁ to 415 ₆ each used for computinga message for a node cause a delay corresponding to a node degree. Forexample, the computers 412 ₁ to 412 ₆ cause a delay equal to a period of9 clocks. In addition, if the decoding apparatus 400 carries out ahigh-speed operation at an operation speed higher than a frequency of100 MHz, the computers 412 ₁ to 412 ₆ cause a further delay equal to aperiod of 3 clocks. Thus, pipelining of a period of 3 clocks isrequired.

That is to say, a time period T1 required by the computation section 412to complete the first computation process is a period of 12 clocks. Thetime period T1 is defined as a period from the start of an operation toread out decoding intermediate results D413 from the decodingintermediate result storage memory 413 to the start of an operation tosupply decoding intermediate results D412 to the decoding intermediateresult storage memory 413 as a result of the first computation processcarried out on the decoding intermediate results D413.

Thus, as the time period T1 lapses since the first read operation (R0)to read out decoding intermediate results D503 from the decodingintermediate result storage RAM 502, the computation section 412 startsan operation to supply six decoding intermediate results D412corresponding to matrix elements set at 1 on respectively the first tosixth rows of the parity check matrix H to the decoding intermediateresult storage memory 413 as a result of the first computation process.In the decoding intermediate result storage memory 413, the decodingintermediate results D413 are supplied to the decoding intermediateresult storage RAM 502 by way of the switch 501 as decoding intermediateresults D501. In the decoding intermediate result storage RAM 502, thedecoding intermediate results D501 are stored at an address used forstoring decoding intermediate results D503 in nine consecutive storeoperations (W0 to W8) on the basis of the control signal D420 ₂.

That is to say, a wait time is needed for 3 clocks time period Tw(=T1−9). The time period Tw is a period from the end of the nineconsecutive read operations (R0 to R8) to read out decoding intermediateresults D503 from the decoding intermediate result storage RAM 502 tothe start of the nine consecutive store operations (W0 to W8) to storedecoding intermediate results D501 in the decoding intermediate resultstorage RAM 502.

In other words, the nine consecutive store operations (W0 to W8) tostore in the decoding intermediate result storage RAM 502 ends after thetime period Tw lapses after the end of the nine consecutive readoperations (R9 to R17) to read out from the decoding intermediate resultstorage RAM 503. That is to say, the time period Tw is required as aperiod between the end of nine consecutive read operations (R9 to R17)to read out from the decoding intermediate result storage RAM 503 andthe start of nine consecutive read operations (R18 to R26) to read outfrom the decoding intermediate result storage RAM 502.

In addition, there have also been proposed some methods including amethod implemented by approximation the sum product algorithm citedbefore. However, these proposed methods lead to deterioration ofperformance.

In the case of the aforementioned sum product algorithm that isimplemented by hardware, as described above, the processing to computemessages each corresponding to an edge (the check-node process, thevariable-node process, the first computation process and the secondcomputation process) can be carried out by adoption of a serial methodwhich, processes of the processing are carried out sequentially oneprocess after another; a full parallel method which, all processes ofthe processing are carried out concurrently at the same time; or aparallel method which, some processes of the processing are carried outconcurrently at one time in an operation.

In the case of the full parallel method or the parallel method forcarrying out P processes concurrently at one time, however, a largevalue of P undesirably entails an increased circuit scale of thecomputation section 412 in particular. In the case of a P value of and acode length of 64,800 for example, the circuit scale of the computationsection 412 may reach 20% of the entire decoding apparatus 400 or 60% ofthe logic circuit excluding memories (for example, the decodingintermediate result storage memory 410, the decoding intermediate resultstorage memory 413 and the reception memory 416) employed in thedecoding apparatus 400 in some cases.

In addition, time periods Tw are required as shown in FIG. 21 as periodsduring which no data is read out from the decoding intermediate resultstorage RAM 502 and the decoding intermediate result storage RAM 503.That is to say, during a time period Tw, no decoding intermediateresults D413 are supplied to the computation section 412 for carryingout the first computation process. Thus, during a time period Tw, thecomputation section 412 is undesirably in an idle state of carrying outno first computation process. In the case of a low node degreeparticularly, the time period Tw becomes relatively long, putting thecomputation section 412 in a long wasteful period of time.

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C. Howland and A. Blanksby, “Parallel Decoding Architectures for LowDensity Parity Check Codes”, Symposium on Circuits and Systems, 2001

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E. Yeo, P. Pakzad, B. Nikolic and V. Anantharam, “VLSI Architectures foriterative Decoders in Magnetic Recording Channels”, IEEE Transactions onMagnetics, Vol. 37, No. 2, March 2001

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T. Zhang, K. K. Parhi, “Joint (3, k)-regular LDPC Code anddecoder/encoder design,” IEEE Transactions on Signal Processing, Vol.52, No. 4, pp. 1065 to 1079, April 2004

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M. M. Mansour, N. R. Shanbhag, “A novel design methodology forhigh-performance programmable decoder cores for AA-LDPC codes,”Proceedings of IEEE Workshop on Signal Processing Systems 2003 (SIPS2003), pp. 29 to 34, August 2003

[Patent Document 1]

Japanese Patent Laid-open No. 2004-364233

DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention

Addressing the problems described above, the present invention providesa decoding apparatus and a decoding method, which are capable ofcarrying out a process to decode LDPC codes with a high degree precisionwhile preventing the scale of the circuit implementing the decodingapparatus from increasing.

Means for Solving the Problems

A decoding apparatus according to the present invention includes a firstcomputation section for carrying out a computation process of a checknode for decoding LDPC codes and a second computation section forcarrying out a computation process of a variable node for decoding LDPCcodes, characterized in that: only the first computation section carriesout processes of N (where N is an integer smaller than an integer P)check nodes at the same time; only the second computation sectioncarries out processes of N variable nodes at the same time; or the firstcomputation section carries out processes of N check nodes at the sametime and the second computation section carries out processes of Nvariable nodes at the same time.

A decoding method according to the present invention includes a firstcomputation step of carrying out a computation process of a check nodefor decoding LDPC codes and a second computation step of carrying out acomputation process of a variable node for decoding LDPC codes,characterized in that: only the first computation step is executed tocarry out processes of N (where N is an integer smaller than an integerP) check nodes at the same time; only the second computation step isexecuted to carry out processes of N variable nodes at the same time; orthe first computation step is executed to carry out processes of N checknodes at the same time and the second computation step is executed tocarry out processes of N variable nodes at the same time.

According to the present invention: only processes of N (where N is aninteger smaller than an integer P) check nodes are carried out at thesame time; only processes of N variable nodes are carried out at thesame time; or processes of N check nodes are carried out at the sametime and processes of N variable nodes are carried out at the same time.

Effect of the Invention

Thus, the present invention provides a decoding apparatus and a decodingmethod, which are capable of carrying out a process to decode LDPC codeswith a high degree precision while preventing the scale of the circuitimplementing the decoding apparatus from increasing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an explanatory diagram showing a parity check matrix H of LDPCcodes.

FIG. 2 is a diagram showing a parity check matrix H including a parityportion forming a lower triangle matrix.

FIG. 3 shows a flowchart representing a procedure for decoding LDPCcodes.

FIG. 4 is an explanatory diagram showing flows of messages.

FIG. 5 is a diagram showing a typical parity check matrix H of LDPCcodes.

FIG. 6 is a diagram showing a Tanner graph corresponding to a paritycheck matrix H.

FIG. 7 is a diagram showing a variable node.

FIG. 8 is a diagram showing a check node.

FIG. 9 is a diagram showing a typical parity check matrix H of LDPCcodes.

FIG. 10 is a block diagram showing a typical configuration of a decodingapparatus for decoding LDPC codes by carrying out node computationprocesses sequentially one process after another.

FIG. 11 is a block diagram showing a typical configuration of acheck-node computer shown in FIG. 10.

FIG. 12 is a block diagram showing a typical configuration of avariable-node computer shown in FIG. 10.

FIG. 13 is a block diagram showing a typical configuration of a decodingapparatus for decoding LDPC codes by carrying out all node computationprocesses at the same time.

FIG. 14 is a block diagram showing a typical configuration of acheck-node computer shown in FIG. 13.

FIG. 15 is a block diagram showing a typical configuration of avariable-node computer shown in FIG. 13.

FIG. 16 is a diagram showing a parity check matrix H divided into aplurality of 6×6 units.

FIG. 17 is a block diagram showing a typical configuration of a decodingapparatus for carrying out six node computation processes at the sametime.

FIG. 18 is a block diagram showing a typical configuration of acheck-node computer shown in FIG. 17.

FIG. 19 is a block diagram showing a typical configuration of avariable-node computer shown in FIG. 17.

FIG. 20 is a block diagram showing a typical configuration of a decodingintermediate result storage memory shown in FIG. 17.

FIG. 21 shows timing charts to be referred to in explanation ofoperations of decoding intermediate result storage RAMs shown in FIG.17.

FIG. 22 is a diagram showing component matrixes corresponds to adecoding intermediate result.

FIG. 23 is a block diagram showing a typical configuration of a decodingapparatus according to a first embodiment of the present invention.

FIG. 24 is a block diagram showing a typical configuration of a decodingintermediate result storage memory shown in FIG. 23.

FIG. 25 shows timing charts to be referred to in explanation ofoperations of decoding intermediate result storage RAMs shown in FIG.24.

FIG. 26 is a diagram showing position of component matrixescorresponding to a decoding intermediate result.

FIG. 27 shows a flowchart representing decoding processing carried outby the decoding apparatus shown in FIG. 23.

FIG. 28 is a block diagram showing a typical configuration of a decodingapparatus according to a second embodiment of the present invention.

FIG. 29 is a block diagram showing a typical configuration of areception memory shown in FIG. 28.

FIG. 30 is a block diagram showing a typical configuration of a decodingintermediate result storage memory shown in FIG. 28.

FIG. 31 shows timing charts to be referred to in explanation ofoperations of a reception memory and a decoding intermediate resultstorage memory.

FIG. 32 is a block diagram showing a typical configuration of a decodingapparatus according to a third embodiment of the present invention.

FIG. 33 is a block diagram showing a typical configuration of a decodingintermediate result storage memory shown in FIG. 32.

FIG. 34 is a block diagram showing a typical configuration of a decodingapparatus according to a fourth embodiment of the present invention.

FIG. 35 shows a flowchart representing decoding processing carried outby the decoding apparatus shown in FIG. 34.

DESCRIPTION OF REFERENCE NUMERALS

414 cyclic shift circuit, 415 computation section, 416 reception memory,1000 decoding apparatus, 1101 cyclic shift circuit, 1102 computationsection, 1103, 1104 decoding intermediate result storage memory, 1105control section, 1202 to 1205 decoding intermediate result storage RAM,1499 control section, 1500 reception memory, 1600 decoding intermediateresult storage memory, 1502, 1503 received-data storage memory, 1602,1603 decoding intermediate result storage memory, 1799 control section,1800 decoding intermediate result storage memory, 1801, 1802 decodinghard determination result storage memory, 1803 decoding softdetermination result storage memory, 2000 cyclic shift circuit, 2001syndrome determination section, 2002 decoding intermediate resultstorage memory, 2003 control section

BEST MODES FOR CARRYING OUT THE INVENTION

Concrete embodiments each applying the present invention are explainedin detail by referring to figures as follows.

FIG. 23 is a block diagram showing a typical configuration of a decodingapparatus implemented by a first embodiment of the present invention asan apparatus for decoding LDPC codes expressed by the parity checkmatrix H shown in FIG. 16.

The decoding apparatus 1000 shown in FIG. 23 employs a cyclic shiftcircuit 414, a computation section 415, a reception memory 416, a cyclicshift circuit 1101, a computation section 1102 including three computers1102 ₁ to 1102 ₃, a decoding intermediate result storage memory 1103, adecoding intermediate result storage memory 1104 and a control section1105. It is to be noted that sections identical with their respectivecounterparts employed in the decoding apparatus 400 shown in FIG. 17 aredenoted by the same reference numerals as the counterparts.

The cyclic shift circuit 1101 receives six decoding intermediate resultsD1104 from the decoding intermediate result storage memory 1104 and sixpieces of received data D417 (that is, LDPC codes) from the receptionmemory 416. In addition, the cyclic shift circuit 1101 also receives acontrol signal D1106 from the control section 1105. The control signalD1106 conveys information (or matrix data) indicating that the matrixelement set at 1 in the parity check matrix H as an elementcorresponding to the decoding intermediate results D1104 is an elementobtained as a result of carrying out some cyclic shift operations on aunit matrix included in the parity check matrix H as a unit matrixincluding the matrix element. In addition, the control signal D1106 alsoconveys information indicating which of the six decoding intermediateresults D1104 and the six pieces of received data D417 are to beselected.

On the basis of the control signal D1106, the cyclic shift circuit 1101selects the six decoding intermediate results D1104 or the six pieces ofreceived data D417 and carries out cyclic shift operations on the sixselected decoding intermediate results D1104 or the six selected piecesof received data D417 in order to rearrange the selected data. Then, thecyclic shift circuit 1101 outputs the upper (first to third row) orlower portion (fourth to sixth row) of the six results of the cyclicoperations carried out on the six selected decoding intermediate resultsD1104 or the six selected pieces of received data D417 as decodingintermediate results D1101 to the computation section 1102.

As mentioned above, the computation section 1102 employs the threecomputers 1102 ₁ to 1102 ₃. The computation section 1102 receives thethree decoding intermediate results D1101 (v) from the cyclic shiftcircuit 1101 as a result of a second computation process carried out bythe computation section 415. In addition, the computation section 1102also receives three decoding intermediate results D1103 from thedecoding intermediate result storage memory 1103. Obtained as a resultthe first computation processes carried out previously by the threecomputers 1102 ₁ to 1102 ₃, the three decoding intermediate resultsD1103 (u_(j)) correspond to matrix elements set at 1 in the upper orlower rows of the component matrix. In the computation section 1102, thethree decoding intermediate results D1101 and the three decodingintermediate results D1103 are supplied to the three computers 1102 ₁ to1102 ₃. In addition, the computation section 1102 also receives acontrol signal D1107 from the control section 1105. In the computationsection 1102, the control signal D1107 is supplied to the threecomputers 1102 ₁ to 1102 ₃. It is to be noted that the control signalD1107 is a signal common to the three computers 1102 ₁ to 1102 ₃.

The three computers 1102 ₁ to 1102 ₃ each have a configuration identicalto the configuration of the computer 412 ₁ shown in FIG. 18. The threecomputers 1102 ₁ to 1102 ₃ carry out the first computation processesaccording to Eqs. (7) and (8) by making use of the decoding intermediateresults D1101 and D1103 in order to find three decoding intermediateresults D1102 (v_(i)). The computation section 1102 stores the threedecoding intermediate results D1102 in the decoding intermediate resultstorage memory 1103. The three decoding intermediate results D1102obtained as a result of the first computation processes carried out bythe three computers 1102 ₁ to 1102 ₃ correspond to respectively threematrix elements set at 1 in the three upper or lower rows of thecomponent matrix.

The decoding intermediate result storage memory 1103 typically employsfour single-port RAMs allowing three decoding intermediate results D1102to be stored in the decoding intermediate result storage memory 1103 orread out from the decoding intermediate result storage memory 1103 atthe same time. The decoding intermediate result storage memory 1103receives the three decoding intermediate results D1102 from thecomputation section 1102 and a control signal D1108 from the controlsection 1105 as a signal for controlling operations to store the threedecoding intermediate results D1102 in the decoding intermediate resultstorage memory 1103 or read out the three decoding intermediate resultsD1102 from the decoding intermediate result storage memory 1103.

On the basis of the control signal D1108, the decoding intermediateresult storage memory 1103 allows the three decoding intermediateresults D1102 received from the computation section 1102 to be storedcollectively in the decoding intermediate result storage memory 1103and, at the same time, three decoding intermediate results D1102 alreadystored in the decoding intermediate result storage memory 1103 to beread out from the decoding intermediate result storage memory 1103 andoutput to the computation section 1102 and the cyclic shift circuit 414as decoding intermediate results D1103. That is to say, the operation toread out the decoding intermediate results D1103 from the decodingintermediate result storage memory 1103 to be supplied to thecomputation section 1102 as well as the cyclic shift circuit 414 and theoperation to write the decoding intermediate results D1102 received fromthe computation section 1103 are carried out at the same time.

It is to be noted that, since the decoding intermediate result storagememory 1103 is used for storing decoding intermediate results D1102originated from edges corresponding to matrix elements set at 1 atintersections of the ith column and rows in the parity check matrix H asa result of the first computation processes carried out by thecomputation section 1102, the required storage capacity of the decodingintermediate result storage memory 1103 is equal to the product of thequantization-bit count of the decoding intermediate results D1102 andthe number of matrix elements set at 1 in the parity check matrix H.

Since the cyclic shift circuit 414, the computation section 415 and thereception memory 416 are identical with their respective counterpartsemployed in the decoding apparatus 400 shown in FIG. 17, theirexplanations are omitted. It is to be noted that the cyclic shiftcircuit 414 carries out cyclic shift operations on six decodingintermediate results D1103, three of which are received by the cyclicshift circuit 414 from the decoding intermediate result storage memory1103 at one time, in order to generate six decoding intermediate resultsD414 to be supplied to the computation section 415.

The decoding intermediate result storage memory 1104 is used for storingdecoding intermediate results D1105, which are received in 6-resultunits from the cyclic shift circuit 1101. The decoding intermediateresults D1105 are stored sequentially in the decoding intermediateresult storage memory 1104 in an address range starting with a firstaddress and decoding intermediate results D1105 already stored in thedecoding intermediate result storage memory 1104 are read out from thedecoding intermediate result storage memory 1104. In addition, sixdecoding intermediate results D415 are also stored sequentially in thedecoding intermediate result storage memory 1104 in the address rangestarting with the first address. Obtained as a result of the secondcomputation process carried out by the computation section 415, the sixdecoding intermediate results D415 correspond to respectively sixcolumns of the parity check matrix H.

That is to say, much like the decoding intermediate result storagememory 410 shown in FIG. 17, decoding intermediate results vcorresponding to the first to sixth columns of the parity check matrix Hare stored at the first address in the decoding intermediate resultstorage memory 1104 as a portion of decoding intermediate resultscorresponding to the columns of the parity check matrix H. In the sameway, decoding intermediate results v corresponding to the seventh totwelfth columns of the parity check matrix H are stored at a secondaddress. By the same token, decoding intermediate results vcorresponding to the thirteenth to eighteenth columns of the paritycheck matrix H are stored at a third address. Thereafter, in the sameway, decoding intermediate results v corresponding to the 19th to 108thcolumns of the parity check matrix H are stored as six decodingintermediate results per address at fourth to eighteenth addresses inthe decoding intermediate result storage memory 1104. In this way, 108decoding intermediate results v are stored in the decoding intermediateresult storage memory 1104.

Thus, the number of words in the decoding intermediate result storagememory 1104 is a quotient obtained as a result of dividing the number ofcolumns 108 (code length of LDPC codes) in the parity check matrix Hshown in FIG. 16 by the number of decoding intermediate results 6.Therefore, the number of words in the decoding intermediate resultstorage memory 1104 is 18.

Decoding intermediate results D415 already stored in the decodingintermediate result storage memory 1104 are read out from the decodingintermediate result storage memory 1104 at the same time. To be morespecific, the decoding intermediate results D415 read out from thedecoding intermediate result storage memory 1104 at the same time aresix decoding intermediate results v corresponding to matrix elements setat “1” in the parity check matrix H as matrix elements associated withdecoding intermediate results u_(j) to be found by a computation section1102 provided at the immediately succeeding stage. The decodingintermediate results D415 read out from the decoding intermediate resultstorage memory 1104 at the same time are supplied to the cyclic shiftcircuit 1101 as decoding intermediate results D1104.

The decoding intermediate result storage memory 1104 typically employssingle-port RAMs allowing six decoding intermediate results that arereadable or writeable. In addition, since decoding intermediate resultsD415 obtained as a result of the second computation process carried outby the computation section 415 are stored in the decoding intermediateresult storage memory 1104, the required storage capacity of thedecoding intermediate result storage memory 1104 is equal to the productof the quantization-bit count of the decoding intermediate results D415and the number of columns in the parity check matrix H (code length ofLDPC codes).

The control section 1105 supplies the control signal D1106 to the cyclicshift circuit 1101 and the control signal D1107 to the computationsection 1102 in order to control the cyclic shift circuit 1101 and thecomputation section 1102. In addition, the control section 1105 alsosupplies the control signal D1108 to the decoding intermediate resultstorage memory 1103, the control signal D421 to the cyclic shift circuit414 and the control signal D422 to the computation section 415 in orderto control the decoding intermediate result storage memory 1103, thecyclic shift circuit 414 and the computation section 415.

Data is circulated in the decoding apparatus 1000 for one decodingprocess in the following order: the cyclic shift circuit 1101 to thecomputation section 1102 to the decoding intermediate result storagememory 1103 to the cyclic shift circuit 414 to the computation section415 and to the decoding intermediate result storage memory 1104. Afterthe decoding apparatus 1000 carries out the decoding process repeatedlya predetermined number of times, the decoding intermediate results D1104obtained as a result of the second computation processes carried out bythe computation section 415 are output as the final decoding result.

FIG. 24 is a block diagram showing a typical configuration of thedecoding intermediate result storage memory 1103 shown in FIG. 23.

The decoding intermediate result storage memory 1103 employs switches1201 and 1206 as well as four decoding intermediate result storage RAMs1202 to 1205 each implemented as a single-port RAM.

Before the sections employed in the decoding intermediate result storagememory 1103 are explained in detail, first of all, a method for storingdata into the decoding intermediate result storage RAMs 1202 to 1205 isexplained.

The decoding intermediate result storage RAMs 1202 to 1205 are each usedfor storing decoding intermediate results D1102 obtained as a result ofa first computation process carried out by the computation section 1102and supplied to the decoding intermediate result RAMs 1202 to 1205 byway of the switch 1201.

To put it concretely, at first to ninth addresses in the decodingintermediate result storage RAM 1202, decoding intermediate resultsD1102 (D1201) corresponding to matrix elements set at 1 on the first tothird rows of the parity check matrix H shown in FIG. 16 are stored in aform of packing (ignoring 0) decoding intermediate results D1102 (D1201)corresponding to matrix elements set at 1 on the rows in the horizontaldirection (or the column arrangement direction).

Let notation (j, i) denote an intersection of the jth row and the ithcolumn in the parity check matrix H shown in FIG. 16. In this case, dataset at 1 in the upper half (or the first to third rows) of a 6×6 unitmatrix included in the parity check matrix H shown in FIG. 16 as acomponent matrix spread throughout a matrix area ranging overintersections (1, 1) to (6, 6) are stored at the first address of thedecoding intermediate result storage RAM 1202. By the same token, dataset at 1 in the upper half of a 6×6 shift matrix included in the paritycheck matrix H shown in FIG. 16 as a component matrix spread throughouta matrix area ranging over intersections (1, 25) to (6, 30) are storedat the second address. The shift matrix in this case is a shift matrixobtained by carrying out a cyclic shift operation on a 6×6 unit matrixby 5 matrix elements in the direction to the right. In the same way,data set at 1 in the upper halves of component matrixes included in theparity check matrix H shown in FIG. 16 are stored at the third to eighthaddresses.

Likewise, data set at “1” in the upper half of a 6×6 shift matrixincluded in the parity check matrix H shown in FIG. 16 as a componentmatrix spread throughout a matrix area ranging over intersections (1,103) to (6, 108) are stored at the ninth address. The shift matrix inthis case is a shift matrix obtained by carrying out a cyclic shiftoperation on a 6×6 semi unit matrix by “1” matrix element in thedirection to the right. The 6×6 semi unit matrix in this case is a semiunit matrix obtained by resetting the matrix element set at “1” on thefirst row of a 6×6 unit matrix to “0”. In this case, the first row ofthe 6×6 shift matrix spread throughout a matrix area ranging overintersections (1, 103) to (6, 108) does not include a matrix element setat “1”. Thus, no data is stored at the ninth address.

By the same token, at the tenth to eighteenth addresses in the decodingintermediate result storage RAM 1202, data set at “1” on the thirteenthto fifteenth rows of the parity check matrix H shown in FIG. 16 arestored. To put it in detail, data corresponding to matrix elements setat “1” in the upper half of a 6×6 shift matrix included in the paritycheck matrix H shown in FIG. 16 as a component matrix spread throughouta matrix area ranging over intersections (13, 7) to (18, 12) are storedat the tenth address. The shift matrix in this case is a shift matrixobtained by carrying out a cyclic shift operation on a 6×6 unit matrixby 5 matrix elements in the direction to the right. By the same token,data set at “1” in the upper half of a shift matrix serving as acomponent of a sum matrix included in the parity check matrix H shown inFIG. 16 as a component matrix spread throughout a matrix area rangingover intersections (13, 13) to (18, 18) are stored at the eleventhaddress. The sum matrix in this case is the sum of a 6×6 unit matrix andthe shift matrix, which is obtained by carrying out a cyclic shiftoperation on a 6×6 unit matrix by “1” matrix element in the direction tothe right.

Likewise, data set at “1” in the upper half of the unit matrix servingas a component of the sum matrix included in the parity check matrix Has a component matrix spread throughout a matrix area ranging overintersections (13, 13) to (18, 18) are stored at the twelfth address.Thereafter, in the same way, data set at “1” in the upper halves incomponent matrixes included in the parity check matrix H are stored atthe thirteenth to eighteenth addresses.

By the same token, at the nineteenth to twenty-seventh addresses in thedecoding intermediate result storage RAM 1202, data each set at “1” onthe twenty-fifth to twenty-seventh rows of the parity check matrix Hshown in FIG. 16 are stored. That is to say, the number of words in thedecoding intermediate result storage RAM 1202 is 27.

In addition, at the first to ninth addresses in the decodingintermediate result storage RAM 1203, decoding intermediate resultsD1102 (D1202) corresponding to matrix elements each set at “1” on thefourth to sixth rows of the parity check matrix H shown in FIG. 16 arestored in a form of packing decoding intermediate results D1102 (D1202)corresponding to matrix elements each set at 1 on the rows in thehorizontal direction or the column arrangement direction.

To put it in detail, data corresponding to matrix elements each set at“1” in the lower half (or the fourth to sixth rows) of a 6×6 unit matrixincluded in the parity check matrix H shown in FIG. 16 as a componentmatrix spread throughout a matrix area ranging over intersections (1, 1)to (6, 6) are stored at the first address in the decoding intermediateresult storage RAM 1203. By the same token, data corresponding to matrixelements each set at “1” in the lower half of a 6×6 shift matrixincluded in the parity check matrix H shown in FIG. 16 as a componentmatrix spread throughout a matrix area ranging over intersections (1,25) to (6, 30) are stored at the second address. The shift matrix inthis case is a shift matrix obtained by carrying out a cyclic shiftoperation on a 6×6 unit matrix by 5 matrix elements in the direction tothe right. In the same way, data corresponding to matrix elements eachset at “1” in the lower halves of component matrixes included in theparity check matrix H shown in FIG. 16 are stored at the third to ninthaddresses.

By the same token, at the tenth to eighteenth addresses in the decodingintermediate result storage RAM 1203, data corresponding to matrixelements each set at “1” on the sixteenth to eighteenth rows of theparity check matrix H shown in FIG. 16 are stored. To put it in detail,data corresponding to matrix elements each set at “1” in the lower halfof a 6×6 shift matrix included in the parity check matrix H as acomponent matrix spread throughout a matrix area ranging overintersections (13, 7) to (18, 12) are stored at the tenth address. Theshift matrix in this case is a shift matrix obtained by carrying out acyclic shift operation on a 6×6 unit matrix by 5 matrix elements in thedirection to the right. By the same token, data corresponding to matrixelements each set at “1” in the lower half of a shift matrix serving asa component of a sum matrix (the sum of a 6×6 unit matrix and the shiftmatrix, which is obtained by carrying out a cyclic shift operation on a6×6 unit matrix by 1 matrix element in the direction to the right)included in the parity check matrix H as a component matrix spreadthroughout a matrix area ranging over intersections (13, 13) to (18, 18)are stored at the eleventh address. Likewise, data corresponding tomatrix elements each set at “1” in the lower half of the unit matrixserving as a component of the sum matrix included in the parity checkmatrix H as a component matrix spread throughout a matrix area rangingover intersections (13, 13) to (18, 18) are stored at the twelfthaddress. Thereafter, in the same way, data corresponding to matrixelements each set at “1” in the lower halves in component matrixesincluded in the parity check matrix H are stored at the thirteenth toeighteenth addresses.

By the same token, at the nineteenth to twenty-seventh addresses in thedecoding intermediate result storage RAM 1203, data corresponding tomatrix elements each set at “1” on the twenty-eighth to thirteenth rowsof the parity check matrix H shown in FIG. 16 are stored. That is tosay, the number of words in the decoding intermediate result storage RAM1203 is 27.

In addition, at the first to ninth addresses in the decodingintermediate result storage RAM 1204, decoding intermediate resultsD1102 (D1203) corresponding to matrix elements each set at 1 on theseventh to ninth rows of the parity check matrix H shown in FIG. 16 arestored in a form of packing decoding intermediate results D1102 (D1203)corresponding to matrix elements each set at 1 on the rows in thehorizontal direction or the column arrangement direction.

Data corresponding to matrix elements each set at “1” in the upper half(the seventh to ninth rows) of a first shift matrix serving as acomponent of a sum matrix (the sum of the first shift matrix and asecond shift matrix. In this case, the first shift matrix is a shiftmatrix obtained by carrying out a cyclic shift operation on a 6×6 unitmatrix by 2 matrix elements in the direction to the right whereas thesecond shift matrix is a shift matrix obtained by carrying out a cyclicshift operation on a 6×6 unit matrix by 4 matrix elements in thedirection to the right) included in the parity check matrix H as acomponent matrix spread throughout a matrix area ranging overintersections (7, 1) to (12, 6) are stored at the first address in thedecoding intermediate result storage RAM 1204. Data corresponding tomatrix elements each set at “1” in the upper half of the second shiftmatrix serving as a component of the sum matrix included in the paritycheck matrix H shown in FIG. 16 as a component matrix spread throughouta matrix area ranging over intersections (7, 1) to (12, 6) are stored atthe second address. In the same way, data corresponding to matrixelements each set at “1” in the upper halves of component matrixesincluded in the parity check matrix H are stored at the third to ninthaddresses.

By the same token, at the tenth to eighteenth addresses in the decodingintermediate result storage RAM 1204, data corresponding to matrixelements each set at “1” on the nineteenth to twenty-first rows of theparity check matrix H shown in FIG. 16 are stored. In the same way, atthe nineteenth to twenty-seventh addresses, data corresponding to matrixelements each set at “1” on the thirty-first to thirty-third rows of theparity check matrix H shown in FIG. 16 are stored. That is to say, thenumber of words in the decoding intermediate result storage RAM 1204 is27.

In addition, at the first to ninth addresses in the decodingintermediate result storage RAM 1205, decoding intermediate resultsD1102 (D1204) corresponding to matrix elements each set at “1” on thetenth to twelfth rows of the parity check matrix H shown in FIG. 16 arestored in a form of packing decoding intermediate results D1102 (D1203)corresponding to matrix elements each set at “1” on the rows in thehorizontal direction or the column arrangement direction.

Data corresponding to matrix elements each set at “1” in the lower half(the tenth to twelfth rows) of a first shift matrix serving as acomponent of a sum matrix (the sum of the first shift matrix and asecond shift matrix. In this case, the first shift matrix is a shiftmatrix obtained by carrying out a cyclic shift operation on a 6×6 unitmatrix by two matrix elements in the direction to the right whereas thesecond shift matrix is a shift matrix obtained by carrying out a cyclicshift operation on a 6×6 unit matrix by four matrix elements in thedirection to the right) included in the parity check matrix H as acomponent matrix spread throughout a matrix area ranging overintersections (7, 1) to (12, 6) are stored at the first address in thedecoding intermediate result storage RAM 1205. Data corresponding tomatrix elements each set at 1 in the lower half of the second shiftmatrix serving as a component of the sum matrix included in the paritycheck matrix H as a component matrix spread throughout a matrix arearanging over intersections (7, 1) to (12, 6) are stored at the secondaddress. In the same way, data corresponding to matrix elements each setat “1” in the lower halves of component matrixes included in the paritycheck matrix H are stored at the third to ninth addresses.

By the same token, at the tenth to eighteenth addresses in the decodingintermediate result storage RAM 1205, data corresponding to matrixelements each set at “1” on the twenty-second to twenty-fourth rows ofthe parity check matrix H shown in FIG. 16 are stored. In the same way,at the nineteenth to twenty-seventh addresses, data corresponding tomatrix elements each set at “1” on the thirty-fourth to thirty-sixthrows of the parity check matrix H shown in FIG. 16 are stored. That isto say, the number of words in the decoding intermediate result storageRAM 1205 is 27.

As described above, the number of words in each of the decodingintermediate result storage RAM 1202 to the decoding intermediate resultstorage RAM 1205 is 27. This number 27 is obtained as follows. The rowweight of the parity check matrix H is 9. This row weight of 9 ismultiplied by the row count of 36 to give a multiplied result (thenumber of matrix elements each set at “1” in the parity check matrix H).The multiplied result is then divided by 3, which is the number ofdecoding intermediate results D1201, which can be read out at the sametime, to give a quotient. Finally, the quotient is further divided by 4,which is the number of the decoding intermediate result storage RAMsemployed in the decoding intermediate result storage memory 1103 toresult in the number 27.

The following description explains details of operations carried out bythe sections employed in the decoding intermediate result storage memory1103 shown in FIG. 24.

When the computation section 1102 carries out a first computationprocess, the decoding intermediate result storage memory 1103 receivesdecoding intermediate results D1102 (u_(j)) obtained as a result of thefirst computation process from the computation section 1102. In thedecoding intermediate result storage memory 1103, the decodingintermediate results D1102 are stored at a predetermined addressdetermined in advance in one of the decoding intermediate result storageRAMs 1202 to 1205. At the same time, from another one of the decodingintermediate result storage RAMs 1202 to 1205, decoding intermediateresults D1102 (u_(j)) obtained as a result of a first computationprocess carried out previously by the computation section 1102 are readout and output to the computation section 1102 as decoding intermediateresults D1103. When the computation section 415 carries out a secondcomputation process, on the other hand, no data is written in thedecoding intermediate result storage RAMs 1202 to 1205 employed in thedecoding intermediate result storage memory 1103. Instead, decodingintermediate results D1102 are read out from an address determined inadvance in one of the decoding intermediate result storage RAMs 1202 to1205 and supplied to the cyclic shift circuit 414 as decodingintermediate results D1103.

The switch 1201 receives three decoding intermediate results D1102 fromthe computation section 1102 and a control signal D1108 ₁ from thecontrol section 1105 as a signal for selecting one of the decodingintermediate result storage RAMs 1202 to 1205 as a RAM to be used forstoring the decoding intermediate results D1102. On the basis of thecontrol signal D1108 ₁, the switch 1201 selects one of the decodingintermediate result storage RAMs 1202 to 1205 and supplies the threedecoding intermediate results D1102 to the selected one of the decodingintermediate result storage RAMs 1202 to 1205.

The three decoding intermediate results D1102 are supplied to thedecoding intermediate result storage RAM 1202 to 1205 as decodingintermediate results D1201 to D1204 respectively. At the same time, thedecoding intermediate result storage RAMs 1202 to 1205 receive controlsignals D1108 ₂ to D1108 ₅ each conveying information on an address fromthe control section 1105. Three decoding intermediate results D1201 toD1204 already stored at an address specified by the control signal D1108₂ to D1108 ₅ as a result of a first computation process carried outpreviously by the computation section 1102 are read out from thedecoding intermediate result storage RAM 1202 to 1205 and supplied tothe switch 1206 as decoding intermediate results D1205 to D1208,respectively. In addition, three decoding intermediate results D1201 toD1204 received from the switch 1201 are stored at an address specifiedby the control signal D1108 ₂ to D1108 ₅ as an address in the decodingintermediate result storage RAM 1202 to 1205, respectively.

The switch 1206 receives the decoding intermediate results D1205 fromthe decoding intermediate result storage RAM 1202, the decodingintermediate results D1206 from the decoding intermediate result storageRAM 1203, the decoding intermediate results D1207 from the decodingintermediate result storage RAM 1204 or the decoding intermediateresults D1208 from the decoding intermediate result storage RAM 1205. Inaddition, the switch 1206 receives a control signal D1086 from thecontrol section 1105 as a signal for selecting one of the decodingintermediate result storage RAMs 1202 to 1205. On the basis of thecontrol signal D1108 ₆, the switch 1206 selects one of the decodingintermediate result storage RAMs 1202 to 1205 as a source for supplyingthe three decoding intermediate results D1205 to D1208, respectively,and outputs the three decoding intermediate results D1205 to D1208, tothe computation section 1102 or the cyclic shift circuit 414 as threedecoding intermediate results D1103.

FIG. 25 shows timing charts referred to in explanation of operations toread out data from the decoding intermediate result storage RAMs 1202 to1205 employed in the decoding intermediate result storage memory 1103and store data into the decoding intermediate result storage RAMs 1202to 1205.

It is to be noted that, in the timing charts shown in FIG. 25, thehorizontal axis represents the lapse of time (t). Notation Rio shown inFIG. 25 denotes an operation to read out data corresponding to a matrixelement indicated by the suffix i₀ enclosed in a circle in the upperhalf of a component matrix shown in FIG. 26 to indicate that the matrixelement is a matrix element set at “1” and notation Wi₀ denotes anoperation to write (store) the above-mentioned data. Further, notationRi₁ denotes an operation to read out data corresponding to a matrixelement indicated by the suffix ii enclosed in a circle in the lowerhalf of a component matrix shown in FIG. 26 to indicate that the matrixelement is a matrix element set at “1” and Wi₁ denotes an operation towrite the above-mentioned data.

When the computation section 1102 carries out a first computationprocess, the decoding intermediate result storage memory 1103 carriesthe following operations. In each of 9 (9 clocks) read operations (R0 ₀to R8 ₀) on the basis of the control signal D1108 ₂, three decodingintermediate results D1201 (D1205) already stored at an address in thedecoding intermediate result storage RAM 1202 are read out from thedecoding intermediate result storage RAM 1202 as decoding intermediateresults D1201 (D1205), which are then output to the computation section1102 as decoding intermediate results D1103 by way of the switch 1206.The three decoding intermediate results D1201 (D1205) correspond tomatrix elements each set at “1” in the first to third rows of the paritycheck matrix H. Since the row weight of the parity check matrix H shownin FIG. 16 is 9, the number of decoding intermediate results D1201 eachcorresponding to a matrix element set at “1” on each row of the paritycheck matrix H is also 9. The decoding intermediate results D1201 eachcorresponding to a matrix element set at “1” on the first to third rowsof the parity check matrix H is read out from the decoding intermediateresult storage RAM 1202 nine consecutive in three unit.

Then, on the basis of the control signal D1108 ₃, in each of 9consecutive read operations (R0 ₁ to R8 ₁ in the figure), three decodingintermediate results D1202 already stored at an address in the decodingintermediate result storage RAM 1203 are read out from the decodingintermediate result storage RAM 1203, which are then output to thecomputation section 1102 by way of the switch 1206. The three decodingintermediate results D1202 correspond to matrix elements each set at “1”in the fourth to sixth rows of the parity check matrix H. The threedecoding intermediate results D1202 are a part of decoding intermediateresults D1202 already stored in the decoding intermediate result storageRAM 1203 as a result of a first computation process carried outpreviously by the computation section 1102.

In this case, a time period T1 required by the computation section 1102to complete a first computation process is a period of 12 clocks. Thatis, the time period T1 is defined as a period from the start of anoperation to read out decoding intermediate results D1103 from thedecoding intermediate result storage memory 1103 to the start of anoperation to supply decoding intermediate results D1102 to the decodingintermediate result storage memory 1103 as a result of a firstcomputation process carried out on the decoding intermediate resultsD1103.

Thus, as the time period T1 lapses since the first read operation (R0 ₀)to read out decoding intermediate results D1205 from the decodingintermediate result storage RAM 1202, the computation section 1102starts an operation to supply three decoding intermediate results D1102corresponding to matrix elements each set at “1” on respectively thefirst to third rows of the parity check matrix H to the decodingintermediate result storage memory 1103 as a result of the firstcomputation process. In the decoding intermediate result storage memory1103, the decoding intermediate results D1102 are supplied to thedecoding intermediate result storage RAM 1202 by way of the switch 1201as decoding intermediate results D1201. In the decoding intermediateresult storage RAM 1202, the decoding intermediate results D1202 arestored at an address used for storing decoding intermediate resultsD1205 in nine consecutive write operations (W0 ₀ to W8 ₀) on the basisof the control signal D1108 ₂.

That is to say, a time period Tw corresponding to 3 (=T1−9) clocks isneeded. As shown in the figure, the time period Tw is a period from theend of the 9 consecutive read operations (R0 ₀ to R8 ₀) to read outdecoding intermediate results D1205 from the decoding intermediateresult storage RAM 1202 to the start of the nine consecutive writeoperations (W0 ₀ to W8 ₀) to store decoding intermediate results D1201in the decoding intermediate result storage RAM 1202. As a result, assoon as the time period Tw lapses since the end of the nine readoperations (R0 ₁ to R8 ₁) to read out data from the decodingintermediate result storage RAM 1203, the nine write operations (W0 ₀ toW8 ₀) to store the data into the decoding intermediate result storageRAM 1202 are completed.

In the decoding intermediate result storage memory 1103, however,decoding intermediate results D1203 associated with matrix elements eachset at “1” on the seventh to ninth rows of the parity check matrix H asdata to be used in a next first computation process have been stored inthe decoding intermediate result storage RAM 1204. Thus, right after thenine read operations (R0 ₁ to R8 ₁) to read out data from the decodingintermediate result storage RAM 1203, nine read operations (R9 ₀ to R17₀) to read data from the decoding intermediate result storage RAM 1204can be carried out.

In addition, after the time period Tw lapses since end of the nine readoperations (R0 ₁ to R8 ₁) to read out data from the decodingintermediate result storage RAM 1203, nine write operations (W0 ₁ to W8₁) to store decoding intermediate results D1202 in the decodingintermediate result storage RAM 1203 are started.

Then, right after the nine read operations (R9 ₀ to R17 ₀) to read outdata from the decoding intermediate result storage RAM 1204, decodingintermediate results D1204 associated with matrix elements each set at 1on the tenth to twelfth rows of the parity check matrix H as decodingintermediate results to be used in the next first computation processare read out from the decoding intermediate result storage RAM 1205 innine read operations (R9 ₁ to R17 ₁). In addition, after the time periodTw lapses since the end of the nine read operations (R9 ₀ to R17 ₀) toread out data from the decoding intermediate result storage RAM 1204,nine write operations (W9 ₀ to W17 ₀) to store decoding intermediateresults D1203 into the decoding intermediate result storage RAM 1204 arestarted.

Then, right after the nine read operations (R9 ₁ to R17 ₁) to read outdata from the decoding intermediate result storage RAM 1205, decodingintermediate results D1201 associated with matrix elements each set at“1” on the thirteenth to fifteenth rows of the parity check matrix H asdecoding intermediate results to be used in the next first computationprocess are read out from the decoding intermediate result storage RAM1202 in nine read operations (R18 ₀ to R26 ₀). In addition, after thetime period Tw lapses since the end of the nine read operations (R9 ₁ toR17 ₁) to read out data from the decoding intermediate result storageRAM 1205, nine write operations (W9 ₁ to W17 ₁) to store decodingintermediate results D1204 into the decoding intermediate result storageRAM 1205 are started. Then, thereafter, the same operations arerepeated.

As described above, in the decoding intermediate result storage memory1103, the decoding intermediate results D1102 corresponding to matrixelements each set at “1” on 3 rows of the parity check matrix H arestored sequentially in the four decoding intermediate result storageRAMs 1202 to 1205. Thus, even if the computation section 1102 requitesthe time period T1 to carry out a first computation process, thedecoding intermediate results D1103 can be output continuously to thecomputation section 1102. As a result, the computation section 1102 iscapable of carrying out a first computation process continuously.

FIG. 27 shows a flowchart to be referred to in explanation of decodingprocessing carried out by the decoding apparatus 1000 shown in FIG. 23.The decoding processing is started typically when received data to bedecoded is stored in the reception memory 416.

The flowchart begins with a step S49. At this step, the control section1105 selects one of the decoding intermediate result storage RAMs 1202to 1205 as a memory from which data is to be read out. The controlsection 1105 selects one of the decoding intermediate result storageRAMs 1202 to 1205 by supplying the control signal D1108 ₆ to the switch1206 (FIG. 24). After the switch 1206 selects the decoding intermediateresult storage RAM 1202 to 1205, on the basis the control signal D1108₆, decoding intermediate results D1205 to D1208 are read out from theselected one of the decoding intermediate result storage RAMs 1202 to1205 in three result units and output to the cyclic shift circuit 414and the computation section 1102 as decoding intermediate results D1103.

After the process of the step S49 is completed, step moves on to a stepS50 at which the cyclic shift circuit 414 concatenates the threedecoding intermediate results D1103 received from (the switch 1206employed in) the decoding intermediate result storage memory 1103 asdata corresponding to the upper half of a component matrix with thethree decoding intermediate results D1103 (u_(j)) also received from theswitch 1206 as data corresponding to the lower half of the componentmatrix, and carries out a cyclical shift operation, then supplying theresult of the cyclical shift operation to the computation section 415.

To put it concretely, the cyclic shift circuit 414 receives decodingintermediate results D1103 from the decoding intermediate result storagememory 1103 in three result units and the control signal D421representing matrix data for the decoding intermediate results 1103 fromthe control section 1105. Then, on the basis of the control signal D421,the cyclic shift circuit 414 concatenates the three decodingintermediate results D1103 corresponding to the upper half of acomponent matrix with the three decoding intermediate results D1103corresponding to the lower half of the component matrix, carries out acyclical shift operation (sorting) and supplies the result of thecyclical shift operation to the computation section 415 as decodingintermediate results D414.

Then, at the next step S51, the computation section 415 carries out asecond computation process and supplies decoding intermediate resultsD415 obtained as a result of the second computation process to thedecoding intermediate result storage memory 1104.

To put it concretely, in the process carried out at the step S50, thecomputation section 415 receives six decoding intermediate results D414from the cyclic shift circuit 414 and six received data D417 from thereceived data memory 416. In the computation section 415, each of thesix decoding intermediate results D414 and each of the six received dataD417 are supplied to one of the six computers 415 ₁ to 415 ₆. Inaddition, the computation section 415 also receives the control signalD422 from the control section 1105. In the computation section 415, thecontrol signal D422 is supplied to the six computers 415 ₁ to 415 ₆.

On the basis of the control signal D422, the six computers 415 ₁ to 415₆ each carry out a second computation process according to Eq. (5) onthe 6 decoding intermediate result D414 and the six received data D417,supplying decoding intermediate results D415 (v) corresponding to rowsof the parity check matrix H to the decoding intermediate result storagememory 1104 as results of the second computation processes.

It is to be noted that, if no decoding intermediate results D1103 havebeen stored in the decoding intermediate result storage memory 1103 forthe received data D417 received from the reception memory 416 because afirst computation process has not been carried out, the computationsection 415 sets the decoding intermediate results u_(j) as initialvalues for execution of a second computation process.

After the process of the step S51 is completed, the flow of the decodingprocessing represented by this flowchart goes on to a step S52 at whichthe decoding intermediate results D415 (v) received from the computationsection 415 in the process carried out at the step S51 are stored at acommon address in the decoding intermediate result storage memory 1104.Then, the flow of the decoding processing represented by this flowchartgoes on to a step S53.

At the step S53, the control section 1105 produces a result ofdetermination as to whether or not the computation section 415 hascarried out the computation process on all decoding intermediate resultsD1104 corresponding to columns of the parity check matrix H. If thedetermination result produced in the process carries out at the step S53indicates that the computation section 415 has not carried out thecomputation process on all decoding intermediate results D1104corresponding to columns of the parity check matrix H, the flow of thedecoding processing represented by this flowchart goes back to the stepS49 in order to repeat the processes explained so far.

If the determination result produced in the process carries out at thestep S53 indicates that the computation section 415 has carried out thecomputation process on all decoding intermediate results D1104corresponding to columns of the parity check matrix H, on the otherhand, the flow of the decoding processing represented by this flowchartgoes on to a step S54 at which, on the basis of the control signal D1106received from the control section 1105, the cyclic shift circuit 1101carries out a cyclic shift operation on the six decoding intermediateresults D1104 (v) received from the decoding intermediate result storagememory 1104 and supplies the result of the cyclic shift operation to thecomputation section 1102 as decoding intermediate results D1101 in threeresult units.

After the process of the step S54 is completed, the flow of the decodingprocessing represented by this flowchart goes on to a step S55 at whichthe computation section 1102 carries out a first computation process andsupplies decoding intermediate results D1102 as the result of the firstcomputation process to the decoding intermediate result storage memory1103.

To put it concretely, the computation section 1102 receives threedecoding intermediate results D1101 (v) from the cyclic shift circuit1101 in the process carried out at the step S54 and three decodingintermediate results D1102 (D1103) (u_(j)) already stored in a processcarried out at a step S57 to be described later as a result of a firstcomputation process carried out previously by the computation section1102. In the computation section 1102, each of the three decodingintermediate results D1101 and D1103 are supplied to one of the threecomputers 1102 ₁ to 1102 ₃. In addition, the computation section 1102also receives the control signal D1107 from the control section 1105. Inthe computation section 1102, the control signal D1107 is supplied tothe three computers 1102 ₁ to 1102 ₃.

On the basis of the control signal D1107, the three computers 1102 ₁ to1102 ₃ each carry out a first computation process according to Eqs. (7)and (8) on the three decoding intermediate result D1101 and D1103,supplying decoding intermediate results D1102 (u_(j)) to the decodingintermediate result storage memory 1103 as results of the firstcomputation processes.

It is to be noted that, if no decoding intermediate results D1103 havebeen stored in the decoding intermediate result storage memory 1103 forthe received data D417 received from the reception memory 416 because afirst computation process has not been carried out, the computationsection 1102 sets the decoding intermediate results u_(dv) at 0. To putit concretely, for example, before received data D417 is decoded, datastored in the decoding intermediate result storage memory 1103 isinitialized to 0 or the computation section 1102 masks an input receivedfrom the decoding intermediate result storage memory 1103 to 0.

After the process of the step S55 is completed, the flow of the decodingprocessing represented by this flowchart goes on to a step S56 at whichthe control section 1105 selects one of the decoding intermediate resultstorage RAMs 1202 to 1205 and outputs the control signal D1108 ₁specifying the selected RAM to the switch 1201 (FIG. 24) employed in thedecoding intermediate result storage memory 1103. On the basis of thecontrol signal D1108 ₁, the switch 1201 selects one of the decodingintermediate result storage RAMs 1202 to 1205 each used for storingdecoding intermediate results D1102 and stores the decoding intermediateresults D1102 to the selected one of the decoding intermediate resultstorage RAMs 1202 to 1205.

After the process of the step S56 is completed, step moves on to a stepS57 at which three decoding intermediate results D1201 to D1204 (D1102)received from the resulting from the switch 1201 in the process carriedout at the step S56 are stored at an address in the selected one of thedecoding intermediate result storage RAMs 1202 to 1205. Then, the flowof the decoding processing represented by this flowchart goes on to astep S58.

At the step S58, the control section 1105 produces a result ofdetermination as to whether or not the computation section 1102 hascarried out the computation process on decoding intermediate resultsD1102 corresponding to all matrix elements each set at “1” in the paritycheck matrix H. If the determination result produced in the processcarries out at the step S58 indicates that the computation section 1102has not carried out the computation process on decoding intermediateresults D1102 corresponding to all matrix elements each set at “1” inthe parity check matrix H, the flow of the decoding processingrepresented by this flowchart goes back to the step S54 in order torepeat the processes explained so far.

If the determination result produced in the process carries out at thestep S57 indicates that the computation section 1102 has carried out thecomputation process on decoding intermediate results D1102 correspondingto all matrix elements each set at “1” in the parity check matrix H, onthe other hand, the control section 1105 ends the execution of thedecoding processing represented by this flowchart.

It is to be noted that the decoding apparatus 1000 carries out thedecoding processing represented by the flowchart shown in FIG. 27repeatedly, and outputs a message D1104 resulting from the last secondcomputation process as the eventual decoding result.

In the decoding apparatus 1000 described above by referring to FIG. 23,the computation section 1102 employs the three computers 1102 ₁ to 1102₃. However, it is also possible to provide a configuration in which,instead of such a computation section 1102, it is the computationsection 415 that employs three computers 415 ₁ to 415 ₃. In such aconfiguration, each second computation process is carried out on threedecoding intermediate results and the decoding intermediate resultstorage memory 1104 is provided with three or more decoding intermediateresult storage memory. It is also possible to provide a configuration inwhich the computation section 1102 employs the three computers 1102 ₁ to1102 ₃ whereas the computation section 415 employs three computers 415 ₁to 415 ₃.

As described above, in the decoding apparatus 1000 described above byreferring to FIG. 23, the decoding intermediate result storage memory1103 employs four decoding intermediate result storage RAMs 1202 to 1205and the computation section 1102 carries out each first computationprocess on three decoding intermediate results. Thus, the scale of thecircuit can be reduced without lowering the operating frequency.

In the conventional decoding apparatus 400 employing six computers 412 ₁to 412 ₆ for example, the number of clocks required by each of thecomputers 412 ₁ to to execute a first computation process is 72. In thedecoding apparatus 1000 employing computers 1102 ₁ to 1102 ₃, on theother hand, the number of clocks required by each of the computers 1102₁ to 1102 ₃ to execute a first computation process is 117, which is 1.6times the number of clocks required by the decoding apparatus 400. Thatis to say, even though the number of aforementioned computers 1102 ₁ to1102 ₃ is half the number of aforementioned computers 412 ₁ to 412 ₆,the number of clocks required by the decoding apparatus 1000 is smallerthan two times the number of clocks required by the decoding apparatus400.

In addition, since the number of clocks required by the computers 415 ₁to 415 ₆ to carry out a second computation process is 59, the time ittakes to carry out one decoding process is 131 (=72+59) in the case ofthe decoding apparatus 400 and 176 (=117+59) in the case of the decodingapparatus 1000. That is to say, the length of time it takes to carry outa decoding process in the decoding apparatus 1000 is about 1.3 times thelength of time it takes to carry out a decoding process in the decodingapparatus 400. In other words, the operating frequency of the decodingapparatus 1000 is about 1.3 times the operating frequency of thedecoding apparatus 400.

In addition, if the number of clocks required to carry out a firstcomputation process is small, the ratio of the length of time it takesto carry out a decoding process in the decoding apparatus 400 to thelength of time it takes to carry out a decoding process in the decodingapparatus 1000 decreases. If the numbers of matrix elements each set at“1” on each row of the parity check matrix H is 4 for example, the ratioof the length of time it takes to carry out a decoding process in thedecoding apparatus 400 to the length of time it takes to carry out adecoding process in the decoding apparatus 1000 is 37/52, that is, thelength of time it takes to carry out a decoding process in the decodingapparatus 1000 is about 1.4 times the length of time it takes to carryout a decoding process in the decoding apparatus 1000.

FIG. 28 is a block diagram showing a typical configuration of a decodingapparatus 1000 according to a second embodiment of the presentinvention.

The decoding apparatus 1000 shown in FIG. 28 employs a reception memory1400 as a substitute for the reception memory 416 employed in thedecoding apparatus 1000 shown in FIG. 23, a decoding intermediate resultstorage memory 1401 as a substitute for the decoding intermediate resultstorage memory 1104 and a control section 1402 as a substitute for thecontrol section 1105. The reception memory 1400 receives a controlsignal D1400 from the control section 1402 as a signal for selecting oneof received-data storage memories 1502 and 1503 (described later byreferring to FIG. 29). The decoding intermediate result storage memory1401 receives a control signal D1401 from the control section 1402 as asignal for selecting one of decoding intermediate result storagememories 1602 and 1603 (described later by referring to FIG. 30).

FIG. 29 is a block diagram showing a typical configuration of thereception memory 1400 shown in FIG. 28.

As shown in FIG. 29, the reception memory 1400 employs switches 1501 and1504 as well as received-data storage memories 1502 and 1503.

The switch 1501 receives data D416 (received data) representing an LLR(Log Likelihood Ratio), which is defined as the value of the 0likelihood of a sign bit computed from received values (or sign bits)received from a communication line. In addition, the switch 1501 alsoreceives a control signal D1400 ₁ from the control section 1105 as asignal for selecting the received-data storage memory 1502 or 1503. Onthe basis of the control signal D1400 ₁, the switch 1501 supplies thereceived data D416 to the received-data storage memory 1502 as receiveddata D1501 or to the received-data storage memory 1503 as received dataD1502.

The received-data storage memory 1502 is used for storing received dataD1501 received from the switch 1501. In addition, received data D1501already stored in the received-data storage memory 1502 is read out fromthe received-data storage memory 1502 and supplied to the switch 1504 asreceived data D1503.

On the other hand, in a way similar to the received-data storage memory1502, the received-data storage memory 1503 is used for storing receiveddata D1502 received from the switch 1501. In addition, received dataD1504 already stored in the received-data storage memory 1503 is readout from the received-data storage memory 1503 and supplied to theswitch 1504.

It is to be noted that the storage capacity of each of the received-datastorage memories 1502 and 1503, that is, the required amount of datathat is to be stored in each of the received-data storage memories 1502and 1503, is equal to the multiplication of the code length of LDPCcodes and the quantization-bit count of the received data.

The switch 1504 receives a control signal D1400 ₂ as a signal forselecting the received-data storage memory 1502 or 1503. On the basis ofthe control signal D1400 ₂, the switch 1504 selects the received dataD1503 read out from the received-data storage memory 1502 or thereceived data D1504 read out from the received-data storage memory 1503and supplies the received data D1503 or the received data D1504 to thecyclic shift circuit 1101 and the computation section 415 as receiveddata D417.

It is to be noted that, if the control signal D1400 ₁ selects thereceived-data storage memory 1502, the control signal D1400 ₂ selectsthe received-data storage memory 1503 or vice versa. That is to say, ifreceived data D1501 is being stored in the received-data storage memory1502, received data D1504 is read out from the received-data storagememory 1503. If received data D1502 is being stored in the received-datastorage memory 1503, on the other hand, received data D1503 is read outfrom the received-data storage memory 1502.

As described above, the reception memory 1400 employs the tworeceived-data storage memories 1502 and 1503. Thus, while received-dataD416 is being stored into one of the two received-data storage memories1502 and 1503, received data already stored in the other one of the tworeceived-data storage memories 1502 and 1503 can be read out from theother one of the two received-data storage memories 1502 and 1503 asreceived data D417. As a result, the reception memory 1400 is capable ofcontinuously outputting received data D416, which is input continuously,as received data D417.

Next, the configuration of the decoding intermediate result storagememory circuit 1401 shown in FIG. 28 is explained in detail by referringto FIG. 30.

As shown in FIG. 30, the decoding intermediate result storage memorycircuit 1401 employs switches 1601, 1604 and 1605 as well as decodingintermediate result storage memories 1602 and 1603.

The switch 1601 receives 3 decoding intermediate results D415 from thecomputation section 415 and a control signal D1401 ₁ from the controlsection 1105 as a signal for selecting one of the decoding intermediateresult storage memories 1602 and 1603. On the basis of the controlsignal D1401 ₁, the switch 1601 selects one of the decoding intermediateresult storage memories 1602 and 1603 and supplies the decodingintermediate results D415 to the decoding intermediate result storagememory 1602 as decoding intermediate results D1601 or to the decodingintermediate result storage memory 1603 as decoding intermediate resultsD1602.

The decoding intermediate result storage memory 1602 is used for storingthe decoding intermediate results D1601 received from the switch 1601.In addition, decoding intermediate results D1601 already stored in thedecoding intermediate result storage memory 1602 are read out from thedecoding intermediate result storage memory 1602 and supplied to theswitch 1604 as decoding intermediate results D1603 and to the switch1605 as decoding intermediate results D1604. In the same way as thedecoding intermediate result storage memory 1602, the decodingintermediate result storage memory 1603 is used for storing the decodingintermediate results D1602 received from the switch 1601. In addition,decoding intermediate results D1602 already stored are read out from thedecoding intermediate result storage memory 1602 and supplied to theswitch 1604 as decoding intermediate results D1605 and to the switch1605 as decoding intermediate results D1606.

It is to be noted that the storage capacity of each of the decodingintermediate result storage memories 1602 and 1603, that is, the amountof data that can be stored in each of the decoding intermediate resultstorage memories 1602 and 1603, is equal to the product of the codelength of LDPC codes for the decoding intermediate result D415 and thequantization-bit count of the decoding intermediate result D415.

The switch 1604 receives a control signal D1401 ₂ from the controlsection 1105 as a signal for selecting one of the decoding intermediateresult storage memories 1602 and 1603. On the basis of the controlsignal D14012, the switch 1604 selects the decoding intermediate resultsD1603 read out from the decoding intermediate result storage memory 1602or the decoding intermediate results D1605 read out from the decodingintermediate result storage memory 1603 and outputs the decodingintermediate results D1603 or the decoding intermediate results D1605 asa decoding result (or a soft determination value) D1402.

By the same token, the switch 1605 receives a control signal D1401 ₃from the control section 1105 as a signal for selecting one of thedecoding intermediate result storage memories 1602 and 1603. On thebasis of the control signal D1401 ₃, the switch 1605 selects thedecoding intermediate results D1604 read out from the decodingintermediate result storage memory 1602 or the decoding intermediateresults D1606 read out from the decoding intermediate result storagememory 1603 and outputs the decoding intermediate results D1604 or thedecoding intermediate results D1606 as a decoding intermediate resultD1403 to the cyclic shift circuit 1101.

It is to be noted that, if the control signal D1401 ₂ selects thedecoding intermediate result storage memory 1602, the control signalD1401 ₃ selects the decoding intermediate result storage memory 1603 orvice versa. That is to say, if decoding intermediate results D1603 arebeing read out from the decoding intermediate result storage memory 1602and output as a decoding result D1402, decoding intermediate resultsD1606 are read out from the decoding intermediate result storage memory1603 and output as a decoding intermediate result D1403. If decodingintermediate results D1605 are being read out from the decodingintermediate result storage memory 1602 and output as a decoding resultD1402, on the other hand, decoding intermediate results D1604 are readout from the decoding intermediate result storage memory 1603 and outputas a decoding intermediate result D1403.

As described above, the decoding intermediate result storage memory 1401employs the two decoding intermediate result storage memories 1602 and1603. Thus, decoding intermediate results D1601 or D1602 being decodedcan be written into one of the two decoding intermediate result storagememories 1602 and 1603 whereas decoding intermediate results D1601 orD1602 completing a decoding process can be stored in the other one thetwo decoding intermediate result storage memories 1602 and 1603. As aresult, a decoding process can be carried out while the decodingintermediate result storage memory 1401 is outputting a decoding resultD1402. Therefore, the decoding intermediate result storage memory 1401is capable of outputting the decoding result D1402 continuously.

FIG. 31 shows timing charts referred to in explanation of operations toread out (or output) data from the reception memory 1400 and thedecoding intermediate result storage memory 1401 and write (or store)data into the reception memory 1400 and the decoding intermediate resultstorage memory 1401.

It is to be noted that, in the timing charts shown in FIG. 31, thehorizontal axis represents the lapse of time (t). In addition, receiveddata #i shown in the timing charts of FIG. 31 is received data D416 ofan ith frame supplied by the reception memory 1400. In addition, in thetiming charts shown in FIG. 31, decoding intermediate result #i is adecoding intermediate result D1403 of received data #i whereas decodingresult #i is a decoding result D1402 of received data #i. In the timingcharts shown in FIG. 31, in a time period between the start of anoperation to receive received data #i and the end of an operation todecode received data #i, a process to decode a piece of received data iscompleted.

When received data #2 is supplied to the reception memory 1400, during atime period Ta required for inputting all received data #2, receiveddata #2 is supplied to the received-data storage memory 1502 by way ofthe switch 1501 to be stored. At that time, received data #2 alreadystored in the received-data storage memory 1503 is supplied to theswitch 1504 to be outputted to the cyclic shift circuit 1101 and thecomputation section 415. Then, received data #1 is decoded.

In addition, the computation section 415 supplies decoding intermediateresults #1 to the decoding intermediate result storage memory 1602employed in the decoding intermediate result storage memory circuit 1401to be stored in the decoding intermediate result storage memory 1602. Ontop of that, decoding intermediate results #1 already stored in thedecoding intermediate result storage memory 1602 are supplied to thecyclic shift circuit 1101. In addition, decoding intermediate results #0already stored in the decoding intermediate result storage memory 1603are outputted to the switch 1604 as decoding result #0. That is to say,during the time period Ta, the decoding intermediate result storagememory circuit 1401 outputs decoding intermediate results #0.

After the lapse of the time period Ta, received data #3 is inputted tothe received-data storage memory circuit 1400 and, during a time periodTb required for inputting all received data #3, received data #3 issupplied to the received-data storage memory 1503 by way of the switch1501 to be stored in the received-data storage memory 1503. At thattime, received data #2 already stored during the time period Ta is readout from the received-data storage memory 1502, being supplied to thecyclic shift circuit 1101 and the computation section 415 by way of theswitch 1504. Then, received data #2 is decoded.

In addition, the decoding intermediate result storage memory 1602outputs decoding intermediate results #1 stored in the decodingintermediate result storage memory 1602 during the time period Ta asdecoding result #1. That is to say, during the time period Tb followingthe time period Ta, the decoding intermediate result storage memory 1602outputs decoding intermediate results #1 from the decoding intermediateresult storage memory 1401 during the time period Ta as decoding result#1. The computation section 415 supplies decoding intermediate results#2 to the decoding intermediate result storage memory 1603 by way of theswitch 1601 to be stored in the decoding intermediate result storagememory 1603. On top of that, decoding intermediate results #2 alreadystored are supplied from the decoding intermediate result storage memory1603 to the cyclic shift circuit 1101.

After the lapse of the time period Tb, received data #4 is inputted tothe reception memory 1400 and, during a time period Tc required forinputting all received data #4, the same processing as that of the timeperiod Ta is carried out. That is to say, during the time period Tcfollowing the time period Tb, received data #3 is supplied to the cyclicshift circuit 1101 and the computation section 415, which then decodesreceived data #3. On top of that, decoding intermediate results #2already stored in the decoding intermediate result storage memory 1603during the time period Tb are outputted as decoding result #2.

As described above, in the decoding apparatus 1000 shown in FIG. 28,consecutively input pieces of received data D417 can be sequentiallydecoded and output continuously as a decoding result. Thus, the decodingprocess can be carried out at a high speed. That is to say, thethroughput of the decoding apparatus 1000 can be increased.

It is to be noted that each of the number of received-data storagememories 1502 (1503) employed in the reception memory 1400 shown in FIG.29 and the number of decoding intermediate result storage memories 1602(1603) employed in the decoding intermediate result storage memorycircuit 1401 shown in FIG. 30 is by no means limited to 2. By increasingeach of the number of received-data storage memories 1502 and decodingintermediate result storage memories 1602, it is possible to increasethe number of times of decoding can be carried out so that the decodingperformance can be improved.

If each of the number of received-data storage memories 1502 anddecoding intermediate result storage memories 1602 is increased to threefor example, one of the received-data storage memories 1502 can be usedfor storing received data D417 and one of the decoding intermediateresult storage memories 1602 can be used for storing a decoding resultD1402. Then, the remaining two received-data storage memories 1502 andthe remaining two decoding intermediate result storage memories 1602 canbe used for carrying out a decoding process. In such a configuration,two computation sections 415 and two computation sections 1102 arerequired, entailing an increased circuit scale. However, it is possibleto double the number of times of decoding can be carried out.

FIG. 32 is a block diagram showing a typical configuration of a decodingapparatus 1000 according to a third embodiment of the present invention.

The decoding apparatus 1000 shown in FIG. 32 employs a decodingintermediate result storage memory 1701 as a substitute for the decodingintermediate result storage memory 1401 employed in the decodingapparatus 1000 shown in FIG. 28 and a control section 1799 as asubstitute for the control section 1402 shown in FIG. 28. The decodingintermediate result storage memory 1701 receives a control signal D1701as a signal for selecting one of decoding hard determination resultstorage memories 1802 and 1803 employed in the decoding intermediateresult storage memory 1701 (as will be described later by referring toFIG. 33). The decoding intermediate result storage memory 1701 outputs ahard determination value of a decoding intermediate result D415resulting from a decoding process as a decoding result D1702 and a softdetermination value of a decoding intermediate result D415 being decodedas a decoding intermediate result D1703.

FIG. 33 is a block diagram showing a typical configuration of thedecoding intermediate result storage memory 1701 shown in FIG. 32.

As shown in FIG. 32, the decoding intermediate result storage memory1701 employs switches 1801, 1805 and 1806, decoding hard determinationresult storage memories 1802 and 1803 as well as a decoding softdetermination result storage memory 1804.

The switch 1801 receives hard determination values of three decodingintermediate results D415 from the computation section 415 as decodinghard determination results D1801 and a control signal D1701 ₁ from thecontrol section 1702 as a signal for selecting one of the decoding harddetermination result storage memories 1801 and 1802. On the basis ofcontrol signal D1701 ₁, the switch 1801 supplies the decoding harddetermination results D1801 to the decoding hard determination resultstorage memory 1802 as decoding hard determination results D1803 or tothe decoding hard determination result storage memory 1803 as decodinghard determination results D1804.

The decoding hard determination result storage memory 1802 is used forstoring the decoding intermediate results D1803 received from the switch1801. In addition, decoding intermediate results D1803 already stored inthe decoding hard determination result storage memory 1802 are read outfrom the decoding hard determination result storage memory 1802 andsupplied to the switch 1805 as decoding intermediate results D1805 andto the switch 1806 as decoding intermediate results D1807.

In the same way as the decoding hard determination result storage memory1802, the decoding hard determination result storage memory 1803 is usedfor storing the decoding intermediate results D1804 received from theswitch 1801. In addition, decoding intermediate results D1804 alreadystored in the decoding hard determination result storage memory 1803 areread out from the decoding hard determination result storage memory 1803and supplied to the switch 1805 as decoding intermediate results D1806and to the switch 1806 as decoding intermediate results D1808.

It is to be noted that the storage capacity of each of the decodingintermediate result storage memories 1802 and 1803, that is, the maximumamount of data that can be stored in each of the decoding intermediateresult storage memories 1802 and 1803, is equal to the product of thecode length of LDPC codes for the decoding intermediate result D415 andthe number of bits in the hard determination value of the decodingintermediate result D415. In this case, the number of bits is 1.

The decoding soft determination result storage memory 1804 receives softdetermination values excluding the most significant bits of threedecoding intermediate results D415 received from the computation section415 as decoding soft determination results D1802. The decoding softdetermination result storage memory 1804 is used for storing thedecoding soft determination results D1802. In addition, decoding softdetermination results D1802 already stored in the decoding softdetermination result storage memory 1804 are outputted as decoding softdetermination results D1811.

It is to be noted that the storage capacity of the 1804, that is, theamount of data that can be stored in the decoding soft determinationresult storage memory 1804, is equal to the product of the code lengthof LDPC codes and the number of bits (the quantization-bit count of thedecoding intermediate result D415-1) in the soft determination valueexcluding the most significant bit.

The switch 1805 receives a control signal D1701 ₂ from the controlsection 1702 as a signal for selecting one of the decoding harddetermination result storage memories 1802 and 1803. On the basis of thecontrol signal D1701 ₂, the switch 1805 selects the decoding harddetermination results D1805 read out from the decoding harddetermination result storage memory 1802 or the decoding harddetermination results D1806 read out from the decoding harddetermination result storage memory 1803 and outputs as a decodingresult (or a hard determination value) D1702.

By the same token, the switch 1806 receives a control signal D1701 ₃from the control section 1702 as a signal for selecting one of thedecoding hard determination result storage memories 1802 and 1803. Onthe basis of the control signal D1701 ₃, the switch 1805 selects thedecoding hard determination results D1807 read out from the decodinghard determination result storage memory 1802 or the decodingintermediate results D1808 read out from the decoding hard determinationresult storage memory 1803 and outputs as a decoding hard determinationresult D1810. The decoding hard determination result D1810 output by theswitch 1806 is concatenated with the decoding soft determination resultD1811 output by the decoding soft determination result storage memory1804 to generate a decoding intermediate result D1703 including thedecoding hard determination result D1810 as the 1 most significant andthe decoding soft determination result D1811 as less significant bits.The decoding intermediate result D1703 is supplied to the cyclic shiftcircuit 1101.

It is to be noted that, if the control signal D1701 ₂ selects thedecoding intermediate result storage memory 1802, the control signalD1701 ₃ selects the decoding intermediate result storage memory 1803 orvice versa. That is to say, if decoding intermediate results D1805 arebeing read out from the decoding hard determination result storagememory 1802 and output as a decoding result D1702 completing a decodingprocess, decoding intermediate results D1808 are read out from thedecoding hard determination result storage memory 1803 and output as adecoding hard determination result D1810. If decoding intermediateresults D1806 are being read out from the decoding hard determinationresult storage memory 1803 and output as the decoding result D1702completing a decoding process, on the other hand, decoding intermediateresults D1807 are read out from the decoding hard determination resultstorage memory 1802 and output as the decoding hard determination resultD1810.

As described above, the decoding intermediate result storage memory 1701employs the two decoding intermediate result storage memories 1802 and1803 used for storing the hard determination value of the decodingintermediate result D415 as well as the decoding soft determinationresult storage memory 1804 for storing the soft determination value ofthe decoding intermediate result D415. The soft determination value is avalue obtained by excluding the most significant bit from the decodingintermediate result D415. Thus, the decoding intermediate result storagememory 1701 merely needs a storage capacity equal to the sum of twice aproduct obtained as a result of an operation to multiply the code lengthof the LDPC codes by 1 bit and a product obtained as a result of anoperation to multiply the code length of the LDPC codes by (thequantization-bit count of the decoding intermediate results D415-1).

Thus, the circuit scale of the decoding apparatus 1000 shown in FIG. 32as an apparatus employing the decoding intermediate result storagememory 1701 can be made small in comparison with the decoding apparatusshown in FIG. 28 as an apparatus employing the decoding intermediateresult storage memory circuit 1401 having a storage capacity equal totwice a product obtained as a result of an operation to multiply thecode length of the LDPC codes by the quantization-bit count of thedecoding intermediate result D415.

FIG. 34 is a block diagram showing a typical configuration of a decodingapparatus 1000 according to a fourth embodiment of the presentinvention.

The decoding apparatus 1000 shown in FIG. 34 employs a syndromedetermination section 2001 having three syndrome determiners 2001 ₁ to2001 ₃. The syndrome determination section 2001 is a unit for carryingout a syndrome computation process on a hard determination result D2000output by a cyclic shift circuit 2000. The decoding apparatus 1000 endsa decoding process on the basis of the result of the syndromeprocessing.

On the basis of a control signal D1106, the cyclic shift circuit 2000selects six decoding intermediate results D1104 or received data D417and carries out a cyclic shift operation to rearrange. The cyclic shiftcircuit 2000 outputs three of the results of the cyclic shift operationto the computation section 412 as decoding intermediate results D1999.The three decoding intermediate results D1999 correspond to matrixelements each set at “1” in the upper (the first to third rows) or lowerhalf (the fourth to sixth rows) of a component matrix. In addition, thecyclic shift circuit 2000 supplies a hard determination result of theresults of the cyclic shift operation carried out on the six decodingintermediate results D1104 or the received data D417 to the syndromedetermination section 2000 as hard determination results D2000.

As described above, the syndrome determination section 2001 has thethree syndrome determiners 2001 ₁ to 2001 ₃. Also as described above,the syndrome determination section 2001 receives the hard determinationresults D2000 from the cyclic shift circuit 2000 and a control signalD2001 for controlling a syndrome computation process from a controlsection 2003. In the syndrome determination section 2001, the harddetermination result D2000 and the control signal D2001 are supplied tothe three syndrome determiners 2001 ₁ to 2001 ₃.

On the basis of the control signal D2001, the three syndrome determiners20011 to 20013 carry out operations to compute syndromes of the harddetermination results D2000. To put it concretely, the three syndromedeterminers 2001 ₁ to 2001 ₃ compute exclusive logical sums (EXOR) ofthe hard determination results D2000 for the rows of the parity checkmatrix H and produce a result of determination as to whether or not theexclusive logical sums are “0” for all the rows. The syndromedeterminers 2001 ₁ to 2001 ₃ supply the determination result D2002 tothe control section 2003.

It is to be noted that the syndrome computation process of the syndromedetermination section 2001 and the first computation process of thecomputation section 1102 can be carried out at the same time.

In accordance with the determination result D2002 received from thesyndrome determination section 2000, the control section 2003 ends thedecoding process. To put it concretely, in accordance with thedetermination result D2002, the control section 2003 supplies a controlsignal D2003 to the decoding intermediate result storage memory 2002 tooutput a decoding intermediate result D415 or a decoding result D1105 asa decoding result. On the basis of the control signal D2003 receivedfrom the control section 2003, the decoding intermediate result storagememory 2002 outputs either of a decoding intermediate result D415 and adecoding result D1105 as a decoding result or supply a decodingintermediate result D415 to the cyclic shift circuit 2000.

FIG. 35 shows a flowchart referred to in explanation of decodingprocessing carried out by the decoding apparatus 1000 shown in FIG. 34.The decoding processing is started typically when received data D416 tobe decoded is stored in the reception memory 416.

First of all, at a step S71, the control section 2003 sets a count valueK to 0. Then, the decoding processing goes on to a step S72. At the stepS72, the syndrome determiners 2001 ₁ to 2001 ₃ employed in the syndromedetermination section 2001 compute syndromes of hard determinationresults D2000 received from the cyclic shift circuit 2000. It is to benoted that, at the step executed for the first time, the syndromedetermination section 2001 receives hard determination results D2000 asa result of a cyclic shift operation carried out on received data D417and computes syndromes of the hard determination results D2000 of thereceived data D417.

After the process of the step S72 is completed, the decoding processinggoes on to a step S73 at which, on the basis of a determination resultsupplied by the syndrome determination section 2001, the control section2003 produces a result of determination as to whether or not thesyndromes are “0”. If the determination result produced in the processcarried out at the step S73 indicates that the syndromes are not “0”,the decoding processing goes on to a step S74.

At the step S74, the control section 2003 produces a result ofdetermination as to whether or not the count value K is at least equalto a number N determined in advance. If the determination resultproduced in the process carried out at the step S74 indicates that thecount value K is smaller than the number N determined in advance, thedecoding processing goes on to a step S75.

The processes of the steps S75 to S84 are identical with the processescarried out respectively at the steps S49 to S58 of the flowchart shownin FIG. 27. Thus, explanation is omitted.

After the process of the step S84 is completed, the decoding processinggoes on to a step S85 at which the control section 2003 increments thecount value K by 1. Then, the decoding processing goes back to the stepS72.

If the determination result at the step S73 indicates that the syndromesare “0”, on the other hand, the decoding processing goes on to a stepS86 at which the control section 2003 outputs a decoding intermediateresult D415 or a decoding result D1105 in the decoding intermediateresult storage memory 2002 as a decoding result, and ends the executionof the decoding processing. It is to be noted that, if the determinationresult produced in the process carried out at the step S71 for the firsttime indicates that the syndromes are “0”, the decoding processing isnot carried out at all at the subsequent steps. In this case, thereceived data D417 (or the decoding result D1105) supplied to thecomputation section 415 is output as it is as a decoding result by wayof the decoding intermediate result storage memory 2002.

If the determination result produced in the process carried out at thestep S74 indicates that the count value K is at least equal to thenumber N determined in advance, on the other hand, the decodingprocessing also goes on to the step S86 at which the control section2003 outputs a decoding intermediate result D415 in the decodingintermediate result storage memory 2002 as a decoding result, and endsthe execution of the decoding processing.

As described above, the execution of the decoding processing shown inFIG. 35 is ended when the syndromes are “0” or the count value K is atleast equal to the number N determined in advance (if the series ofdecoding processes carried out at the steps S72 to S85 has been executedN times). It is thus possible to prevent the number of errors fromincreasing again because the decoding intermediate result D415 with “0”syndromes or an error count of 0 is further decoded. In the case ofreceived data with a large SN (Signal Noise) ratio of the received dataD416, it is a so possible to suppress the number of times the decodingprocesses are carried out so as to prevent the decoding performance fromdeteriorating. Thus, the power consumption of the decoding apparatus canbe reduced.

It is to be noted that, in general, the circuit scale of the syndromedetermination section 2001 is so small that it is possible to ignore acircuit scale increase caused by incorporation of the syndromedetermination section 2001 in the decoding apparatus 1000.

In addition, the decoding apparatus 1000 shown in FIG. 34 is obtained byadding the syndrome determination section 2001 to the decoding apparatus1000 shown in FIG. 23. The syndrome determination section 2001 can beadded to any decoding apparatus if the decoding apparatus is anapparatus for carrying out a decoding process by execution ofcomputation processing at two phases (such as the check-node process andthe variable-node process or the first computation process and thesecond computation process). For example, the syndrome determinationsection 2001 can be added to the decoding apparatus 400 shown in FIG. 17and the decoding apparatus shown in FIG. 28 or 32.

In the embodiments of the present invention, the decoding intermediateresult storage memory 1103 employs four decoding intermediate resultstorage RAMs 1202 to 1205. The number of decoding intermediate resultstorage RAMs 1202 to 1205 can be set at any arbitrary value as long asthe value is at least equal to three. The larger the number of decodingintermediate result storage RAMs 1202 to 1205, the higher the processingspeed of the decoding apparatus.

In addition, in the embodiments of the present invention, the decodingprocessing is carried out by executing the first computation process andthe second computation process repeatedly. However, the decodingprocessing can also be carried out by executing the check-node processand the variable-node process repeatedly.

If the number of bits in a physical RAM employed in each of the decodingintermediate result storage RAMs 1202 to 1205 shown in FIG. 24, thereceived-data storage memories 1502 and 1503 shown in FIG. 29, thedecoding intermediate result storage memories 1602 and 1603 shown inFIG. 30 as well as the decoding hard determination result storagememories 1802 to 1803 and the decoding soft determination result storagememory 1804, which are shown in FIG. 33, is not sufficient, a pluralityof physical RAMs can be employed. In this case, the same control signalis supplied to the plurality of RAMs so that the employed RAMs can behandled as a single RAM.

In the embodiments described above, the value of P is set at six inorder to make the explanation simple. That is to say, in the embodimentsdescribed above, the number of rows and the number of columns in each ofcomponent matrixes composing the parity check matrix H are each 6.However, the value of P, that is, the number of rows and the number ofcolumns in each component matrix, do not have to be six. For example,the value of P can be set at a value peculiar to the parity check matrixH. Typical values of P are 360 and 392.

In addition, in the embodiments of the present invention, the LDPC codeshave a code length of 108 and a coding rate of ⅔. However, the LDPCcodes can have any arbitrary code length and any arbitrary coding rate.In the case of a parity check matrix H including component matrixes eachhaving a row count of 6 and a column count of 6 for example, any LDPCcodes with any arbitrary code length and any arbitrary coding rate canbe decoded by the decoding apparatus 1000 by merely changing a controlsignal provided that the number of all edges is six or smaller.

On top of that, a decoding apparatus for decoding LDPC codes satisfyingconditions is capable of decoding LDPC codes with any arbitrary codelength and any arbitrary coding rate provided that the LDPC codessatisfy the conditions. In this case, the conditions require that therow count P and column count P of each component matrix shall have avalue determined in advance whereas the number of all edges shall not begreater than a certain value.

If the number of rows and/or the number of columns of each componentmatrix are not a multiple of the row count P or the column count P,additional rows and additional columns with all matrix elements set at 0are attached to the matrix H so that the number of rows and/or thenumber of columns in the matrix H become a multiple of the row count Por the column count P. In some cases, the decoding apparatus provided bythe present invention is used for decoding LDPC codes defined by such anexpanded parity check matrix H.

In the decoding apparatus 1000 described earlier, the number ofcomputers 1102 ₁ to 1102 ₃ employed in the computation section 1102 isthree (=P/2). However, the number of computers employed in thecomputation section 1102 can be set at any arbitrary value as long asthe value is smaller than the value of P. Even if the value of P is alarge prime number, the number of computers 1102 ₁ to 1102 ₃ can be setat a prime number close to an integer 1.

Instead of designing the computation section 1102 employed in thedecoding apparatus 1000, the computation section 415 can be designed asa section having a plurality of computers, the number of which issmaller than the value of P. That is to say, at least one of thecomputation section 1102 and the computation section 415 need to bedesigned as a section having a plurality of computers, the number ofwhich is smaller than the value of P. In this case, the other one of thecomputation section 1102 and the computation section 415 is designed asa section having a plurality of computers, the number of which issmaller than or equal to the value of P.

By adoption of the architecture described above, P or N (where N is apositive integer smaller than the value of P) first and secondcomputation processes can be carried out at the same time in order tosuppress the operating frequency to a value in a range that can beimplemented. In addition, the decoding processing can be carried outrepeatedly a large number of times. On top of that, it is possible toprevent accesses to different addresses from being made at the same timein operations to write data into a memory (which can be a FIFO memory ora RAM) and read out data from the memory. As described above, in thearchitecture, P or N first and second computation processes are carriedout on LDPC codes defined by a parity check matrix H. The parity checkmatrix H is a matrix that can be represented as a combination of P×Punit matrixes, semi unit matrixes, shift matrixes, sum matrixes and P×P0 matrixes. The semi unit matrix is a matrix obtained by setting one ormore of the matrix elements each having a value of 1 in a unit matrix to0. The shift matrix is a matrix obtained by carrying out a cyclic shiftoperation on a unit matrix or a semi unit matrix. The sum matrix is amatrix obtained by computing the sum of a plurality such matrixes.

In addition, by carrying out N first or second computation processes atthe same time, the number of computers 1102 ₁ to 1102 ₃ composing thecomputation section for carrying out a first computation process or thenumber of computers 415 ₁ to 415 ₆ composing the computation section 415for carrying out a second computation process can be reduced to a valuesmaller than the computer counts of a configuration in which P first andsecond computation processes are carried out at the same time. Thus, thecircuit scale of the decoding apparatus can be reduced.

In general, the code length of LDPC codes is a value in a range ofseveral thousands to several tens of thousands. Thus, a large P value inthe order of several hundreds is used. In this case, the effect ofmaking use of the decoding apparatus provided by the present inventionis even greater.

In addition, the decoding apparatus provided by the present inventionfaithfully adopts the sum product algorithm. Thus, a decoding loss otherthan the quantization of the message is not incurred.

From the above points of view, by making use of the decoding apparatusprovided by the present invention, high-performance decoding processingcan be carried out.

It is to be noted that the decoding apparatus for decoding LDPC codes asdescribed above can be applied to, for example, a tuner for receiving(digital) satellite broadcasts.

1. A decoding apparatus for LDPC (Low Density Parity Check) codesdefinable by a parity check matrix including a combination of at leastone component matrix which can be a P×P (where P is a positive integer)unit matrix, a semi unit matrix obtained by setting one or more ofmatrix elements each having a value of 1 in said unit matrix to 0, ashift matrix obtained by carrying out a cyclic shift operation on saidunit matrix or said semi unit matrix, a sum matrix obtained by computingthe sum of a plurality of said unit matrixes, said semi unit matrixes orsaid shift matrixes, or a P×P 0 matrix, said decoding apparatuscomprising: a first computation section configured to carry out acheck-node computation process in order to decode said LDPC codes; and asecond computation section configured to carry out a variable-nodecomputation process in order to decode said LDPC codes; wherein onlysaid first computation section carries out N (where N is a positiveinteger smaller than said P) said check-node computation processes atthe same time, only said second computation section carries out N saidvariable-node computation processes at the same time, or said firstcomputation section carries out said N check-node computation processesat the same time whereas said second computation section carries outsaid N variable-node computation processes at the same time.
 2. Thedecoding apparatus according to claim 1 wherein said N is an integerequal to a fraction of said P.
 3. The decoding apparatus according toclaim 1 wherein said first computation section carries out saidcheck-node computation process and a portion of said variable-nodeprocess, said second computation section carries out the rest of saidvariable-node computation process, and only said first computationsection carries out said N check-node computation processes and aportion of said variable-node computation processes at the same time,only said second computation section carries out the rest of said Nvariable-node computation processes at the same time, or said firstcomputation section carries out said check-node computation processesand a portion of said variable-node computation processes at the sametime whereas said second computation section carries out the rest ofsaid N variable-node computation processes at the same time.
 4. Thedecoding apparatus according to claim 1 wherein only said firstcomputation section has said N check-node computers each used forcarrying out said check-node computation process, only said secondcomputation section has said N variable-node computers each used forcarrying out said variable-node computation process, or said firstcomputation section has said N check-node computers each used forcarrying out said check-node computation process whereas said secondcomputation section has said N variable-node computers each used forcarrying out said variable-node computation process.
 5. The decodingapparatus according to claim 4 wherein if said first computation sectionhas said N check-node computers, each of said N check-node computerssequentially inputs second computation results produced by said secondcomputation section from said second computation section, and each ofsaid N check-node computers sequentially outputs first computationresults of said check-node computation process carried out by making useof said second computation results, and if said second computationsection has said N variable-node computers, each of said N variable-nodecomputers sequentially inputs first computation results produced by saidfirst computation section from said first computation section, and eachof said N variable-node computers sequentially outputs secondcomputation results of said variable-node computation process carriedout by making use of said first computation results.
 6. The decodingapparatus according to claim 2 further comprising: a first storagesection configured to store first computation results produced by saidfirst computation section; and a second storage section configured tostore second computation results produced by said second computationsection; wherein said first storage section allows said N firstcomputation results to be stored in said first storage section at thesame time and to be read out, or said second storage section allows saidN second computation results to be stored in said second storage sectionat the same time and to be read out.
 7. The decoding apparatus accordingto claim 6 wherein said first storage section stores said firstcomputation results by packing matrix elements each set at 1 in saidparity check matrix, which defines said LDPC codes, in a row direction.8. The decoding apparatus according to claim 6 wherein said firststorage section includes a plurality of memories allowing said N firstcomputation results to be stored at the same time and to be read out, orsaid second storage section includes a plurality of memories allowingsaid N second computation results to be stored at the same time and tobe read out.
 9. The decoding apparatus according to claim 6 wherein saidfirst storage section stores said N first computation results obtainedfor a plurality of matrixes obtained as a result of decomposing said summatrix into said unit matrixes, said semi unit matrixes or said shiftmatrixes at an address common to said N first computation results, andsaid second storage section stores said N second computation resultsobtained for a plurality of matrixes obtained as a result of decomposingsaid sum matrix into said unit matrixes, said semi unit matrixes or saidshift matrixes at an address common to said N second computationresults.
 10. The decoding apparatus according to claim 2 furthercomprising a rearrangement section configured to rearrange p said firstor second computation results, select N said first or second computationresults from said P first or second computation results and output saidN first or second computation results.
 11. The decoding apparatusaccording to claim 10 wherein said rearrangement section is a parallelshifter.
 12. The decoding apparatus according to claim 1 furthercomprising: a plurality of received-information storage sectionsconfigured to store LDPC codes as received information; a plurality ofcomputation-result storage sections configured to store a computationresult produced by said second computation section; and a storagecontrol section configured to control said received-information storagesections and said computation result storage sections; wherein saidstorage control section executes control to select one of saidreceived-information storage sections as a storage section to store saidreceived information to be used in a later decoding process, read outsaid received information to be used in a present decoding process fromanother one of said received-information storage sections, read out adecoding result of decoding said LDPC codes from one of saidcomputation-result storage sections, and make use of another one of saidcomputation-result storage sections in a present decoding process. 13.The decoding apparatus according to claim 12 wherein said storagecontrol section changes said received-information storage section to beused for storing said received information to be used in a laterdecoding process every time said received information with an amountcorresponding to the code length of said LDPC codes is stored in saidreceived-information storage section.
 14. The decoding apparatusaccording to claim 12 wherein said storage control section changes saidcomputation-result storage section, from which a decoding result ofdecoding said LDPC codes is to be read out, every time said receivedinformation with an amount corresponding to the code length of said LDPCcodes is stored in said selected received-information storage section.15. The decoding apparatus according to claim 1 further comprising: aplurality of received-information storage sections configured to storeLDPC codes as received information; a plurality of hard determinationvalue storage sections configured to store a hard determination value ofa computation result produced by said second computation section; a softdetermination value storage section configured to store a softdetermination value of a computation result produced by said secondcomputation section; and a storage control section configured to controlsaid received-information storage sections and said hard determinationvalue storage sections; wherein said storage control section executescontrol to select one of said received-information storage sections as astorage section to store said received information to be used in a laterdecoding process, read out said received information to be used in apresent decoding process from another one of said received-informationstorage sections, read out a decoding result of decoding said LDPC codesfrom one of said hard determination result storage sections, and makeuse of another one of said hard determination result storage sections ina present decoding process.
 16. A decoding method for LDPC (Low DensityParity Check) codes definable by a parity check matrix comprising acombination of at least one component matrix which can be: a P×P (whereP is a positive integer) unit matrix; a semi unit matrix obtained bysetting one or more of matrix elements each having a value of 1 in saidunit matrix to 0; a shift matrix obtained by carrying out a cyclic shiftoperation on said unit matrix or said semi unit matrix; a sum matrixobtained by computing the sum of at a plurality of said unit matrixes,said semi unit matrixes or said shift matrixes; or a P×P 0 matrix, saiddecoding method comprising: a first computation step, implemented by acheck-node computation section, of carrying out a check-node computationprocess in order to decode said LDPC codes; and a second computationstep, implemented by a variable-node computation section, of carryingout a variable-node computation process in order to decode said LDPCcodes, whereby: only said first computation step is executed to carryout N (where N is a positive integer smaller than said P) saidcheck-node computation processes at the same time; said secondcomputation step is executed to carry out said N variable-nodecomputation processes at the same time; or said first computationsection is executed to carry out said N check-node computation processesat the same time whereas said second computation step is executed tocarry out said N variable-node computation processes at the same time.